Biting is tough; my oldest went through a stage at just over a year and it was very difficult to train him out of it. It took around four months to get him to stop; he just didn't understand it was wrong, even with books, 'Ouch, Biting Hurts', giving more attention to the bitee, etc.
Biting at three is a bit different, though. A three year old has some (limited) understanding that what they're doing is wrong. However, the three year old also has some understanding of his or her situation; it's possible that the child who your child bites (and bites your child) is indeed a bully, and your child doesn't see any good way to solve the problem except by retaliating.
I would put this primarily in the teachers' laps. In particular, if it's just one other child, it should be up to them to watch these two (watch your son until they figure out which other child it is) and ensure they don't get too close (or, whatever seems to set it off doesn't come to pass; perhaps they play together reasonably until one of them wants a toy the other has, or similar.) This probably won't be forever; it might just be a few weeks or a month or two, until both children learn it is not going to work.
They should have enough teachers to watch like this; even if it's multiple classes together on the playground, at least in the US there are minimum standards for numbers of teachers per student (where I live, no more than 15 kids together and at least 1/7 ratio at that age if it's all 3+). If they aren't willing to do this, then it's time to consider another daycare.
Secondly, at home it sounds like you're doing the right thing. Talk to him about it, find out what's going on (to the extent you can). Teach him coping strategies for dealing with bullies. Roleplay the situation; imagine the other child bit him, now, what's the right solution? Not biting, but going to the teacher, or if he doesn't feel comfortable with that, walking away. We struggle with this right now with our oldest, as our youngest just turned one and is still very hard for him to get along with (destructive play primarily); roleplaying helped some, at least, although walking away from his favorite toy can be hard to do.
Also consider books. This book is what we use; it's fairly young-aimed (often used at 1 year old level) but is still quite appropriate for 3 and helps with the role-playing and alternative strategies elements.