I don't know how universally known and used the expression 'bite the bullet' is, though it appears to be understood in both the US and UK. Looking at various online dictionaries you get a definition of to start to deal with an unpleasant or difficult situation which cannot be avoided and this is pretty much how I've always understood the phrase.
Certainly, when it appeared in Rudyard Kiplings 1891 novel The Light That Failed, it was tied to the idea of bearing something with fortitude. As the main character hears, ‘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.’ Notably, this is the first instance of 'bite the bullet' to appear in print.
Where the idiom comes from, as with many such, is unclear. There is, however, indication that it, or at least a a version, was known in the eighteenth century, as Francis Grose’s A Classical Dictionary of the Vulgar Tongue, 1796 makes clear:
Nightingale. A soldier who, as the term is, sings out at the halberts. It is a point of honour in some regiments, among the grenadiers, never to cry out, or become nightingales, whilst under the discipline of the cat of nine tails; to avoid which, they chew a bullet.
To make clear what is being discussed here, a soldier's punishment could be in the form of flogging with a whip called the cat o' nine tails which consisted of a long stiff stem of rope which gave way to nine separate strands, the result of the rope being unwound into its smaller constituent parts. A soldier recieving such a punishment would be bound to a frame of halberts - more commonly spelt halberd - these were long poles with a spike topped axe on the head.
Having been bound to the frame with his back bared it was a matter of pride to bear the punishment without crying out in pain - doing otherwise could earn the soubriquet of nightingale. To help a soldier control his cries they would be offered something to bite down on which made clenching their jaws shut that bit easier. Strips of leather, such as a belt or shaving strop, were known to be used but, as Grose records, a bullet may also be offered. The 12 guage (about 18mm) soft lead ball in general use at the time would give a good size object which could easily be moved around the mouth to allow for varying where the pressure could be applied by the teeth.
All of that being said, biting the bullet in this circumstance doesn't really give the idea of choosing to begin something unpleasant, but more enduring consequences which arises from your own actions, as the flogging was a punishment for the soldier's wrong-doings.
As such I, personally, don't feel that this can be root of the expression as we understand it.
There is also a suggestion that the term was used during the US civil war of 1861-5, with Harriet Tubman relating a soldier being given a bullet to bite on while a limb amputation occured. However, chloroform was already being used as a basic anasthetic and this event is likely to have been an oddity as opposed to a standard practice which then gave rise to a common-ish saying. And again, as with the flogging, it's not so much getting on with something unpleasant, but enduring something unpleasant being done to the person.
Now, there is another nineteenth century event which may have been a tributary to the development of the term, though it would throw a different light on how the saying should be understood.
As military hardware advanced in the eighteenth and nineteenth centuries armaments changed extensively. During the early-to-mid eighteen hundreds older fashioned muskets were being replaced by newer, more accurate, rifles. This was because the rifling, spiral grooves in the gun barrel, imparted spin to the bullet which allowed it to fly further and straighter. To achieve this the bullet had to be wrapped in something which would grip the rifling as it was expelled down the barrel.
This was achieved by enclosing the projectile, and it's propellant into a paper cartridge which was then sealed with a grease which would both provide some protection, and grip the rifling grooves. To prepare for the firing the rifle would be placed on the ground butt first, tear open by biting the cartridge, pour the gunpowder contained within down the barrel, snap off the greased end of the cartridge containing the bullet and place in the muzzle, ram it home, bring up the rifle to the hip, replace the percussion cap, and prepare to fire.
When the Pattern 1853 Enfield was supplied to the Sepoy army in India a rumor arose that the grease on the cartridge was pork lard, beef tallow, or a mixture of the two. For Muslim and Hindu soldiers this felt like an attack on their religious principles, which was excacerbated by their having been an uptick in a view that the natives should be Christianised by some senior leaders in both the East Indies Company and Britain's ruling circles.
Knowing of the issues, and in an attempt to quell any flashpoints, various options were attempted to not only demonstrate the rumors to be untrue, but also to allow the local soldiers to prepare ammunition in a way they would confirm did not violate any religious beliefs.
But the rumors refused to die.
In a turn of events that even shortly after appeared to be unneccessary, Lieutenant Colonel George Munro Carmichael-Smyth had a squad of ninety skirmishers from the 3rd Bengal Light Cavalry parade, and they were instructed to prepare cartridges.
From contemporaneous reports here is little question or doubt that these cartridges were definitely not contaminated with animal fats of any type yet, of the ninety men, eighty-five refused the order. In her excellent website Mutiny Reflections, Eva Chatterji reveals court-martial records saying, 'One of the men went so far as to say, “I know of no objection to them, but yet I have a doubt in my heart.”
The eight-five men who refused to partake in the exercise for fear of a percieved violation of their religious principles were ceremonially stripped, chained, and given ten years of hard labour as punishment.
There is no indication that a specific order was given for the men to 'bite the bullet' or, more accurately, cartridge. But they were in a position where that was the expected outcome of the exercise. Here's the thing, for these men to 'bite the bullet' would be to go against their own fundamental beliefs and to be seen doing so. In choosing to follow conscience and not orders they knew they placed themselves at legal jeapordy, though few would have expected the excessive opprobrium brought on them, still, they followed their conscience and not their conscience violating orders.
Outrage at their treatment led to the prison they were held in being stormed, and the men freed.
Biting the bullet is a phrase, an idiom, which expects the user to do something hard, difficult, unwanted. And when that something is paying a duly incurred speeding or parking fine, getting root canal treatment, or pretending to enjoy your partners hobby, then maybe the stiff upper lip fortitude of Rudyard Kiplings Dickie is suitable.
But in a situation where you are being told to overlook the morals and principles you live by, or to ignore the written code or constitution of your organisation, company, even country, then maybe the example of those eighty-five soldiers is the better one to follow.
Original writing and graphics by stuartcturnbull. Header produced in Canva Pro.