OK - I have just come through this "phase" and I promise to you it is a "phase"; albeit, a long one in our case. I, finally, removed DS2 from nursery because he bit every single child and they had me in but couldn't come up with any strategy to prevent it. Not that I am judging because nor could I .
He went onto school, four months later - they start incredibly early here. The teacher was forewarned and horrified. Despite taking a chunk out of most of his class last year, he is actually quite popular - I think even four-year-olds like rebels .
It is horrible because you feel partly to blame - you are not. I bet you don't go round biting. In DS2's case, it was, unfortunately, a very effective way of communicating anything negative - so hunger, tiredness, annoyance, get-out-of-my-way, and partly, I don't want to be here. Gradually, and I do mean that, he stopped. He still occasionally uses this arm in his weaponry but it is now very unusual.
Just keep doing what you are doing. Forewarn friends you may have to do a runner, if taking him away from the scene of the crime proves helpful, or makes you feel better. He will grow out of it.