Welcome to the Forum. There is no risk for HIV or any other infection from this event. In adults HIV is transmitted only through unprotected sexual intercourse with a genital partner or injection of infected material immediately deep into tissue. The virus is very fragile and even if the person who used the bike before you have HIV and cut themselves, the virus would have become non-infectious immediately upon exposure to the air.
There is no reason for concern and no reason for testing related to the events you have described. EWH
Sorry for the typo
Have = gave