Another wonderful example of police logic. What if it was the Queen of England? Might could have caused an international incident leading to a world war, so we better give him the death penalty.
Improper Backing (Florida Law)
316.1985 Limitations on backing.--
(1) The driver of a vehicle shall not back the same unless such movement can be made with safety and without interfering with other traffic.
(2) The driver of a vehicle shall not back the same upon any shoulder or roadway of any limited access facility.
(3) A violation of this section is a noncriminal traffic infraction, punishable as a moving violation as provided in chapter 318.
History.--s. 1, ch. 71-135; s. 1, ch. 76-31; s. 149, ch. 99-248.
If parallel parking is allowed, why is backing from one space to the one behind it improper? You need to look at the traffic laws in your state and see if there is any possible justification for this citation. Under Florida law, the cop would probably argue that the backing maneuver was clearly "unsafe" because a collision resulted. But if no damage was done, what was so unsafe about it?
He needs to go to court and contest this, whatever the fine is. If the "bump" resulted in damage to another vehicle, this will be taken care of by the insurance companies. The police do not need to be involved. If everyone one would take every single one of these nuisance citations to court, the cost would outweigh the money raked in from fines, and the harassment would end. DON'T BE VICTIMIZED!
UPDATE: OK, you are being victimized by a cop who is not only a bullying jerk, he is a lying sack of poo.
For one thing, the police usually will refuse to participate in minor bumps in a parking lot on the grounds that "We can't get involved when it's on private property." He was probably insulted because he was being forced to take up his valuable time by filling out a police report, so he decided to make you pay for it. I have been in this situation and was required to go to the police station, sit around for an hour, and wait for someone to fill out a report.
For another thing, the cop is not qualified to do a damage estimate. Obviously. Under no stretch of the imagination would a mirror bracket cost $1800 to repair. This absurd affirmation on the police report is evidence of ignorance, at best, and a false statement, at worst.
Thirdly, this "illegal backing" crap is for public streets, NOT private parking lots.
Finally, the cop did not see this happen and should not be extrapolating an illegal act from this kind of evidence. He will probably claim that you admitted doing something illegal, which I hope you did not. You were very careful. (Forget about that thing with the window being steamed up, please.) The bike was too short to be visible and was where it should not have been. You're very sorry, but accidents happen.
With the help of an attorney, you could almost certainly get this whole ridiculous thing dismissed and, if there were anything like justice, the court cost should be assigned to the police department. But as we all know, justice is a rare commodity. Police departments all over this country, especially state police, are milking motorists like dairy cows to the tune of at least $15 billion dollars a year to subsidize their own worthless existence. The cop gets brownie points for writing the ticket even if it is completely fraudulent. When it gets dismissed they don't take away his suck points, so what does he care? Used to be they had to go to court on their own time -- now they get rewarded by overtime when someone gets outraged enough to dispute their abusive charges.
If you don't want to pay an attorney, you have the right to defend yourself. It's not as easy as it looks, but you can do it. Get your evidence together, dress appropriately, and be very careful what you say. Pictures of the motorcycle, and of your vehicle, together with something showing the cost of a new mirror bracket are very good. Also a picture of the parking lot. You were aware of the motorcycle, because of course you looked behind your vehicle before backing up. When you got close to it you could not see it any more, and you accidentally went about 6 inches too far. This kind of thing happens all the time with motorcycles. They are just too damned small.
Then there is always the possibility that the cop will decide to get drunk instead of showing up for court and the whole phony thing will be dismissed. If he remembers it at all, he must remember that he lied like a dog, anticipating that you would just bend over and let him rape you like 99.9% of everyone else does.