Alright Peoples, stand aside and make way for the ex-claims manager. Right now, [rolls up sleeves.. lol]:
1) Neither Jonny who was driving the car or his parents are obligated to repair your bike for you; however they are obligated to reimburse you the cost of repairs or compensate you to the value of the bike if it's beyond economic repair. Alternatively, they may be "indemnified" by an insurance company if there was a policy in force that covers the accident (I'm having to guess that there is, as I don't know the circumstances of the accident).
2) If they will be allowing their insurers to deal with your claim, then they are obligated by the terms of their policy to not admit liability - doesn't mean they're not to blame, simply means that as they won't be dipping into their pockets for you, they don't have the right to go around saying "yes, it was us, we'll pay you" - if they want the insurers to pay then the insurers want them to keep their mouths shut and not (metaphorically) write cheques that the insurer then has to honour.
3) If you claim off their insurance then you can do it in 1 of 2 different ways: claim off your policy first and your insurers will get their money back off their insurers; you'll probably have to pay an excess, which your insurer MAY get back for you at the same time they get reimbursed, or it may have to be claimed back separately. Alternatively you can claim directly off Jonny/his parents insurance, although, again, they aren't obligated to do anything until you've suffered a financial loss, e.g. organised the repairs yourself and paid the bill - they don't have to organise the repairs for you if they don't want to. Some insurers would prefer 3rd parties come to them direct, as it keeps costs lower and they know they aren't getting ripped off with inflated labour charges or costs for hire vehicles, others (the stupider ones) will tell you you're not their customer so they aren't going to help organise repairs; just send them proof of how much it cost.
4) Witnesses need to be idependent, i.e. not someone from your house, Johnny's house or in his vehicle etc. Any non-independent witness carries no weight whatsoever.
5) Lastly, again I don't know what happened in the accident or where, but private property or public road makes no difference as this is a civil matter. The only difference it could make is that if it happened on private property then it could have been the case that the car wasn't insured as he didn't legally need to be, but as there does seem to be an insurance company involced, that's not the case.