A 1796 publication titled  A Classical Dictionary of the Vulgar Tongue by Francis Grose was a book of slang terms for the day and in it appeared the phrase bite the bullet.  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. But there are other theories, perhaps ones you have heard before, and you can read about them here .  These days when we say bite the bullet we are saying that we or someone else needs to fortify self and prepare for the impending difficulty or pain that is coming. 

The phrase first appeared in Shakespeare's 1593, Henry VI Part I, "So Orke must sit and fret and bit his tongue." ( source ) The meaning of the phrase is to keep quiet, stop oneself from saying something rude or regretful, etc.

   I found two different sources about the origin of this phrase. One source said it originated with tobacco , the other source says it was due to taking a bite that was entirely too big for one's mouth . Regardless of the origin of the phrase being due to food or tobacco the meaning today is that someone has agreed to do something more than they can handle.

The meaning of this phrase seems pretty apparent. A dog that barks and barks and barks but never follows it through with an actual bite is not as scary as it may seem. According to Wiktionary  the phrase officially means: (idiomatic) Full of big talk but lacking action, power, or substance; pretentious, (idiomatic) Describes someone who often says cutting remarks, but actually has a soft personality underneath.

The origin of this phrase is unknown. It was first seen in print in the 18th century when political writer Edmund Burke said “having looked to government for bread, on the first scarcity they will turn and bite the hand that fed them.” ( source ) Based on that, and the definition which includes the idea that biting the hand that feeds you is a way to say disrespect is being shown to the person providing necessities, the following are some examples of the phrase.