Bises usually means kisses on the cheeks and is the kind of closing you write to someone you precisely kiss that way in real life (family, close / female friends, female colleagues). This kind of kiss is usually quite formal and not real kisses. People just touch cheeks to each other and kiss the air a specific number of times, usually two but can be one, three of four depending on the region.

Bisous is more friendly and affectionate, and are real kisses where the lips touch the skin. Bisous is generally used when writing to children or between lovers.

There are many people for whom I might end a postcard with Bises or Grosses bises but who would be very surprised if I wrote instead Bisous or Gros bisous.

Bisous is for very close people like family / girlfriend…

Young french people say la bise to their friends at the end of their messages

I’ve never seen Bises without la in a message