Ok, I'll bite (pun intended)

Just so you know where I'm coming from, I'm a part-time instructor of OC (pepper spray) and firearms, and I'm an armorer. This isn't to brag, its so you understand my mindset.

Falls and discharges- It would take a very rare set of circumstances and some very stupid decisions to have a gun go off in a fall. It would be no accident, it would be negligence. Guns go in holsters, or alone in their carry compartment of a backpack. If anything else is crammed in the bag with it that could get inside the trigger guard, then they are an idiot and made a mistake.
Modern guns will not fire, due to a mechanical break, when dropped. They will only fire when the safeties (active and passive) are activated and the trigger is pressed. If you think the gun will go off when dropped, then I suggest you read up on the subject. You will be pleasantly surprised.

I'll add that all modern firearms that I can think of are designed to be safely carried with a round in the chamber. You would be amazed at all the things that go on in that short trigger pull to allow the firing pin to strike the primer.

Accuracy - That depends on the shooter. The muzzle blast alone will usually dissuade non-committed attackers, both human and animal. Its much louder than a yell and feels like a slap across the face, even from the 9mm. I wouldn't want to shoot from my bike while still moving, unless I absolutely had to, but if I did, it would be reasonably accurate at such close ranges.

Be ready to stop the rest of your day to spend time with the police, most of it in handcuffs, while they figure out the details behind why you discharged your firearm.

OC - The best choice for most people. Its non-lethal, temporary and VERY painful. You can get them in a variety of sizes, trigger styles, chemical compositions and dispersal patterns. There are fogs, streams, cone-shaped sprays, foams, gels and probably a lot more that I'm forgetting. Things to consider are backsplash (when it bounces off the opponent and gets on you), innocent bystanders, decontamination, of you and/or anyone else, impaired driving and cycling abilities after being sprayed (or caught up in the cloud), etc.
It is unwise to think that you can just spray that stuff and ride away. Most anytime you spray it, you will catch some, either with the backsplash or when it is still hanging in the air. If it catches you, you won't be able to see or think as straight as normal. It could be as slight as a tingle in your eye and a scratch in your throat, or you will be just as incapacitated as the guy who you sprayed. Don't believe me? I highly suggest you try it out. Go into the garage and spray something (trashcan, etc.) from your bike. Take a few deep breaths like you would if in an actual event, then open the garage door and ride around the block. Better yet, have someone spray you in the face with it. Just a little bit, so you know how it feels and how you will react to it.

I haven't used either a gun or OC from the bike, and I usually get away with just yelling at the dog, but I have been known to carry something when I ride.

Hope this helped