If you bite down on a bullet then nothing would happen as your bite would not be strong or hard enough to actually set off the bullet.
In the old days people were given a bullet to bite down on for their pain before they had a lot of medicine and I guess the bullet being bit down on provided them with pain relief due to the pressure they were putting on the bullet.
A human would not be able to bite down hard enough to actually cause the bullet to go off so there's no worry there.
As long as you do not swallow the bullet then you're not gonna be harmed when biting down on a bullet and it may help with pain.
However I would rather take pain medicine instead for the pain than trying to bite down on a bullet.