You can have no claims bonus on more than one vehicle, it is just insurers do not like you knowing. You can easily insure two separate vehicles and accumulate no claims on each vehicle, but what insurers do not like you doing is using the same no claims bonus on more than one vehicle. Some insurers will credit it to you, especially if you put both cars on the same policy. This is the insurer con, the con being insurers already have all of your details on their underwriting database called CUE.

The specific question insurers ask is, "can you provide proof of no claims" as long as no fraud, lies or deception takes place, and you do indeed have the no claims you state you have, then the insurer would have to accept what you provide them. This can be proof of no claims from your previous insurer up to three year ago. It is however very rare an insurer will credit no claims bonus from a bike to a car, why this is, I have no idea, aside from I see it as another insurer con.