my nephew was a biter! My brother and SIL had to watch him like a hawk every minute. It meant that they missed out on a lot of grownup time at parties, etc. but it was the only way once he had gotten the habit.
We all learned to look for his 'tells'. When he started to get over tired or just excited, his voice would get louder, his eyes would get sort of glassy and he would just get this 'look' in his eye - you could see it, if you watched for it! After he took a chunk out of grandpa's arm, we all knew the signs, lol.
At that point, his mom or dad or someone would swoop him up and take him someplace quiet and tell him that he needed to calm down before he could go back to play. It wasn't punishment or even a time out- but just down time to calm him down. Even my son, who is a little older, got to know the signs and would come running up to us saying " He's getting ready to bite again!"
Once he was in preschool full time, he sort of stopped on his own. his mom and dad had him tested for everything. ADD, etc. but there was never any real reason for it. But the routine of school and the structure just seemed to really suit him and it all just went away- now he is a very very bright, well-adjusted elementary school boy, but they were really going crazy for a while!
I would say also, make sure you TELL your family and friends and other parents you are going through this! Don't be embarrassed or try to hide it. It happens! Let other grownups know to be on the watch and avoid an incident rather than having to do damage control afterwards- same for preschool teachers, etc. People will be more sympathetic if they know you are aware of the issue and trying to do something about it.
Last but not least- this is what I did when my 10 year old was little. He bit me ONE time- really really hard. I shrieked and nearly dropped him out of my lap and he had this little grin- he just thought it was really funny. He went to do it again and I took his arm and bit it, very slowly, until it started to hurt. As soon as he said OW and started to pull away, I stopped and said
"Biting HURTS. We NEVER bite. You hurt mommy when you did that!" I showed him my bite mark and asked " Did it hurt when mommy bit you?" He sniffed a yes and we both compared our bite marks and promised to never ever bite anything but our food ever again!
And it worked- he never again bit me or anyone else. I am not saying it is the best approach for you- but that is what worked for me! Good luck!