For the enthusiasts or followers of the practice of greeting friends by giving a “bise” it’s been a tradition for at least the past 50 years to abide by the “friend of yours is a friend of mine” rule or some other rule that remains unacknowledged, and so is common the distribution of kisses to all present in a group where at least one person is by force of precedents entitled to that privilege; often, the custom is not that of giving just one “bise” but instead two, one on each cheek, or even three, four or five, changing from cheek to cheek for each new kiss in the series — it’s complicated; however, let’s make things quite clear: it’s not a practice you’ll witness in any group of persons knowing one another ; as years went on this behaviour has been extended to new types of groups but initially it was found among the young, the adolescents, and I suspect that even before its generalisation to groups comprising both boys and girls it was restricted to groups of girls or to the girls in the mixed groups. Typical groups are those of school friends, those of people participating together in sports events, groups of young people partying; for instance, that practice does not impinge upon groups based essentially on family ties: a stranger in such a group will not be sollicited to do that because no such custom exists for those groups.
So, if you happen to be in such a “bise” group, and know not at all a person suddenly joining it, whether that person is a male or a female, if he/she knows someone closely enough for this sort of greetings, you can expect that you also will be greeted that way, nevertheless only after at least one of those in the group for whom this is usual has been kissed; this priority principle, as it is in harmony with the principle that, roughly, bonds of camaraderie are reasserted first with those who enjoy a greater seniority in someone’s frienship, serves at the same time the necessity of not being too intrusive upon a total stranger and, so to speak, in preparing them to a ritual that will appear more natural; there is almost never any hesitation on the part of the persons in such situations, neither from the kiss giver nor from the receiver, no soul searching as to the legitimacy of the act, no squeamishness. It was said above that one cannot be certain as to what really motivates this practice; the rather coldly reasoned attitude based on the “transitivity” of friendship is only a vague possibility. The practice can be seen as confering, apparently, feelings of great frienship and those given to the practice of greeting their friends with kisses may have feelings of guilt in the sense of having an impression that a discriminatory behaviour towards those they should treat differently, more formally, could be interpreted in a negative way. The practice could thus have sprung from an egalitarian concern. One must not forget either the easiness with which such acts of greeting can be performed: there is nothing to say and most of the time no verbal exchange will accompany them; it’s done rapidly and you can go on quickly to someone else to whom you don’t really have anything to say. Therefore, this aspect is possibly also a source of motivation.

To answer this particular question of yours, “Is she being creepy?”, I’ll say, most likely, no, she isn’t; she is probably in a group where her behaviour is nothing but more or less usual.

I can’t see what could be wrong in comparing the American hug and the French bise, except if by “comparing” you must mean that they represent two behaviours that correspond exactly; that is far from the truth; as to comparing them point by point, why not do that? It’s certainly an interesting exercise for a number of research workers versed in questions of civilisation, human behaviour, sociology, anthropology and what not. I’ll barely skim the surface and advance one answer easy to arrive at, possibly all that a layman would wish to know. The bise custom is a rather regular thing and every new day asks for one new “bise” (at least for a certain number of days in a row given the context) whereas the american hug is not; it’s something that Americans do after fairly long separations for instance or in great occasions, as in times of rejoycing about great achievements, and that they do in times of great sorrow, particularly when it has been overcome. We touch here, I think, upon one of the essential differences. The American hug, if it should be called so, is a much more emotional act. One must understand that the American hug is maybe not any more so strictly American or that it has possibly never been so, as women, mostly, among themselves can be seen hugging themselves in all parts of the world in the same contexts (those just mentioned).

As my comments show, the one armed-hug and the two-armed hug have their equivalent except that the one-armed hug is not a hug but a kiss or two and that the two-armed hug is not a practice found among men, only women are given to it among themselves or with men. It is not usual to use your arms or even only one in an act of giving a “bise” such as the one described in the contexts considered above.

Don’t try to compare these habits between cultures. You’ll rarely find exact equivalents.

In France, you shake hands or kiss cheeks the first time you meet a person in a day. Kissing cheeks is considered exactly equivalent to shaking hands in terms of familiarity, and can be done the very first time you meet someone.

Between friends or colleagues, it’s common that two men shake hands, but two women or a woman and a man kiss cheeks. Within a family, men often kiss cheeks. Men kiss cheeks in some communities but that’s relatively uncommon. Cheek kissing is usually not practiced even between women in formal settings when not meeting friends, for example it would be unusual in a business meeting.

Cheek kissing can involve any number from 1 to 5 kisses (on alternate cheeks). It’s complicated. It’s mostly regional, but not completely, and can occasionally get awkward when people used to different cheek counts meet.

Inasmuch as I understand US hugging habits, cheek-kissing is closer to the American one-armed hug and there’s no equivalent to the two-armed hug. A hug in France is either a lot more intimate, or an expression of sympathy rather than a greeting (“I’m sorry for your loss”, “I hope you’re feeling better”, …).

is it something else entirely?

Yes.

Is it utterly wrong to compare faisant la bise in France with an American hug?

Yes. Faire la bise or shaking hands are equivalent to the contactless good morning/hello/hi in the US. When doing the bise, the cheeks touch together but the lips generally stay in the air, unless there is also an expression of affection like withing a family or close friends. Note that there is an emerging trend for women to avoid the every morning bise to all colleagues at work and just shake hands like what is done between men. See https://www.sudouest.fr/2018/01/04/quand-les-femmes-en-ont-assez-de-faire-la-bise-au-travail-4083352-5458.php Shaking a woman’s hand was once considered rude but is now becoming the norm at work.

Anyone have any experience where they are different?

In the US you shake hands once when you are introduced or being introduced to someone and that’s it. You might give a hug or shake hands when leaving for a long time, or when meeting again after a while but outside that, there is far less physical contact between people. In France, we touch dozens of people hands or cheeks every day.

See also this article about "social kissing* in the US:
https://www.nytimes.com/2012/07/22/fashion/social-kissing-welcome-or-not.html?pagewanted=all

and that question too https://workplace.stackexchange.com/questions/5658/should-i-shake-hands-with-everyone-at-the-start-of-the-day

2021 Update: Needless to say, habits have changed tremendously since March 2020. I haven’t touched any cheek or hand for almost one year (except my close family’s, i.e. sharing the same house). I suspect this change is here to stay.

Is she doing a “any friend of so-and-so is a friend of mine!” sort of
thing

This, or an “everyone treated equal” / “everyone is part of the group” sort of thing – not giving the bise to the third person may make them feel set aside. You might also come across as inappropriately distant and not very chaleureux if you don’t.

Of course, the usual precautions apply – what’s on people’s minds may vary considerably. Greeting habits are hardly uniform across all Americans or all French.

or is she being creepy

In that particular instance, no – why would she? She isn’t any creepier than you are when hugging a friend’s friend, probably even less so. Of course, a bise to a complete stranger on the street would in contrast be as creepy as a hug indeed.

Is it utterly wrong to compare faisant la bise in France with an
American hug?

Compare in what regard? As other answers have pointed out, they are quite different things. Bises are far more ubiquitous than American hugs to begin with. Just because rounds of bises and hugs are both usually extended to friends’ friends doesn’t mean they carry the same symbolic meaning or intention.

Obviously, nowadays nobody "fait la bise", but in prepandemic times it was fairly common to "faire bisous" (an expression that I am personally more familiar with). In fact, it was the most common form of greeting between women or a man and a woman – much rarer between men, outside of professional environment. Faire bisous to total strangers is something that I observed on many occasions, although this did not seem a universal rule.

Thus, I would say that it used to be much more common than a hug in the American culture. For more cultural comparisons I could also add that, being Russian, I didn’t have reflex even for kissing the family membets, which was not always correctly understood.