Accept the inevitable impending hardship and endure the resulting pain with fortitude.
Origin
I've always believed that, before the days of effective anaesthetics, soldiers were given bullets to bite on to help them endure pain. 'I've always believed' has to be as poor an opening gambit as 'it is widely accepted' or 'a man in a pub told me' on a piece discussing the origins of a phrase.
Is it true or is it just 'believed'? The theory goes that patients undergoing surgery would be given a stick of wood or a pad of leather to bite on in order to concentrate their attention away from the pain and also to protect against biting their own tongues. A bullet, being somewhat malleable and not likely to break the patient's teeth, is said to have been an impromptu battlefield alternative. Lead poisoning would probably have been a secondary concern in those circumstances.
An ingenious correspondent has suggested that, as wooden sticks are known as billets, the stick-biting practice might have first been called 'biting the billet' which then modified to 'biting the bullet'. Worth investigating certainly. My initial enthusiasm was dampened rather by finding that no records of the phrase 'bite the billet' can be found in historical newspapers and other records. That would have been a neat solution but, lacking any supporting evidence, it seems best to discount it.
Many artists, notably Rembrandt Van Rijn and Hieronymus Bosch, painted scenes of early surgery and none of those paintings shows patients biting into anything. Whether or not they might have been offered anything to nibble on, there's little doubt that they would have been fortified with strong drink.
The most frequently cited origin of the alleged 'biting the bullet' practice is the American Civil War. This seems rather improbable, as effective anaesthesia using ether and chloroform was introduced in 1846/47 and ether was issued to U.S. military surgeons as early as 1849 - well before the US Civil War began in 1861. The photograph to the right shows, albeit not too clearly, a patient undergoing amputation in a US Civil War field hospital, with a cloth, presumably soaked in ether/chloroform, held near his mouth. It doesn't look like much fun but, given the choice, and apparently they were, surely patients would prefer unconsciousness to bullet chewing.
On the other hand (isn't there always an other hand?), there is a record of an interview with a Mr. Fergusson in the literary magazine The West of England Miscellany, Volume 1, Issue 1, 1844:
The instant chance of being killed, in fact, and never more seeing Mrs. Ferguson, was eminently disagreeable to me. I shook a little, I confess, and bit the bullet-end of my cartridge, saying my prayers of course, the first time for ten years.
That may well be a fictional account rather than an actual battlefield memory, but it does place the usage of 'bit the bullet' in 1844 and I can find no earlier example. It doesn't really match the figurative meaning of the phrase though as refers to an attempt to allay fear rather than pain. Early muzzle-loading firearms were loaded from paper cartridges which contained a charge of powder and a bullet. Soldiers ripped the cartridges open with their teeth and poured in the powder, followed by the bullet. This is where the term 'cartridge paper' derives incidentally. 1844 seems to be rather late for the use of such a weapon but the account may well be a later fictionalised one and reference to a cartridge does suggest that it was merely the loading of a gun that was being described.
It seems unlikely that surgical patients ever bit bullets. However, it doesn't have to have been a description of something that actually happened for a phrase to pass into metaphorical use; the belief that it referred to some real practice would be sufficient. Rudyard Kipling wrote a dialogue in the 1891 novel The Light That Failed, which uses the expression figuratively (there is no actual bullet involved in the scene), but which appears to allude to the idea, real or invented, that fortitude can be gained by biting a bullet:
'Steady, Dickie, steady!' said the deep voice in his ear, and the grip tightened. 'Bite on the bullet, old man, and don't let them think you're afraid.'
By 1926, the phrase had left the gory battlefields of the Boer War far behind and moved into the drawing rooms of the English upper classes, in the voice of Bertie Wooster, speaking to Jeeves in The Inimitable Jeeves, 1923:
Brace up and bite the bullet. I'm afraid I've bad news for you.
My 'always believed that' is now looking distinctly shaky - time for me to bite the bullet and accept the inevitable I think.