“Should have” is something you didn’t do, you would translate it this way :

J’aurais dû partir plus tôt [pour être à l’heure à la réunion]

“must have” is something you did, and had no choice, you would translate it this way :

J’ai dû partir plus tôt [pour aller chercher ma fille à l’école]

“would have” is something you didn’t do, but you couldn’t, you would translate it this way :

Je serais parti plus tôt [si j’avais pu]

Thanks for the reply @Random.

It’s been awhile now, but in response to your question @Eria – we use “must have” quite often in English, but not actually in the manner described by @Random. “J’ai dû” could be translated two different ways in English, depending on what it means:

1. “Had to” – Something you did, having no other choice. I would concur with your translation of “J’ai dû partir plus tôt” (I had to leave sooner/earlier).

2. “Must have” – Something that we know/think happened a certain way, based on inference.

For instance, if my friend had the flu when we met up, and soon after I fell sick as well, he might say to me:

“J’ai dû te la refiler!” (I must have given it to you!)

I hope it makes more sense in that context.