Here's what I found so far:
BITE THE BULLET -- "Brace yourself for an unpleasant experience; decide to get on with a difficult task. Although one can find other explanations, it seems most plausible that the term originated in battlefield surgery before the days of anesthesia. A surgeon about to operate on a wounded soldier would urge him to bite on a bullet of soft lead to distract him from the pain; at least it would minimize his ability to scream and thus divert the surgeon. Rudyard Kipling reflected the broader meaning in 'The Light that Failed' (1890): "Bite on the bullet, old man, and don't let them think you're afraid.'" From "The Dictionary of Cliches" by James Rogers (Ballantine Books, New York, 1985).