If you are like me then you most probably said something silly when selling the bike like "give me a shout if anything goes wrong". This is why I should never be a salesman. Procurement manager for sure but not a salesman.

What it boils down to is this: I could have bought your scooter off you and then ridden it like it was stolen for the next couple of days. Well good old me I had a bit of fun but I managed to bugger the engine up in that time - now I'll just go and take the seller up on that nice little promise they gave me when I bought it.

So - even if you did say something to that effect, you should just try to help him ruling out obvious stuff (have you put the key in it etc..) but in no way offer any money to fix. Any private sale is "as is, where is" hence the point of test rides (unless you are a member of the MTA, like most bike shops - which you are not). You sound like a good person but don't let people take advantage of you.