Lots of good suggestions already.
The only thing I can add is that sometimes a baby just needs to be really hungry and then they will take a bottle. I compare it to an adult - e.g. you want to eat dinner, but there are only leftovers, so you think "no, I don't want that". An hour later, however, those leftovers look more appetising. Sometimes babies can be the same, i.e. they know that if they refuse the bottle they will get the breast. However, when the breast still doesn't come after a while, they will take the bottle.
Also - I have found andecdotally that babies are super smart and they kind of know when the bottle is the only option vs when they know that mum is close by...