If a tree falls in the forest and there is no one there to hear it, does it make a sound? Sound is a wave traveling through the air that enters the ear and vibrates the eardrum (the tympanic membrane). The wave is there when the tree falls, whether the eardrum is there or not.
Alienator, you are correct that listening to music while riding can serve to distract the bicyclist. Listening to music while driving can distract a motorist. I am not certain that I would put it in the same category as talking on a cell phone. Music can exist in the background and not require the same level of attention as maintaining a conversation on a phone.
Your description of the workings of the ear is essentially correct. The sound wave vibrates the eardrum. On the inside side of the ear drum there is a chamber filled with fluid and three very small bones, the ossicles. For those of you interested in evolution, they were the second, third, and fourth gill slits in our very primitive ancestors. The ossicles transmit the vibrations from the eardrum to the cochlea. The fluid that is contained within the middle ear has a somewhat high inertia, and would not transmit the vibrations as well.
The face plate of the third bone, the stapes, rests against the cochlea. The vibrations of the stapes creates a pressure wave within the cochlea and the frequency of that wave will correspond to the resonant frequency of some of the hair cells, causing them to vibrate and sending nerve impulses telling the brain the frequency and intensity of the sound wave. Repeated exposure to loud noise will somewhat deaden the hair cell responding to the frequency of that noise, resulting in temporary or permanent hearing loss in that frequency. There are other types of hearing loss. I personally suffer from a conductive hearing loss. There is a problem with my ossicles that prevents them from conducting sound as efficiently as a normal person's. I am basically hard of hearing at all frequencies.
The outer circumference of the cochlea's face is anchored to the skull. A vibration in the skull bone will vibrate the cochlea and stimulate the corresponding hair cells. Bone conduction hearing aids and headphones are not magic. They operate by bypassing the eardrum and ossicles and transmitting the sound vibration directly to the cochlea via the skull.
Although it is possible that my listening to music while riding may distract me, my use of bone conduction headphones allows me to hear traffic noises as well as I would be able to hear them if I was not listening to music.
I am currently retiring after twenty years of working on Navy nuclear power plants and I am a Nationally Registered Radiation Protection Technologist. I already know a lot of words that are bigger and more impressive than douchebag. I have been called several of them.