Risks for HIV are:
1) Having unprotected penetrative anal or vaginal sex, OR
2) Sharing IV drug equipment with other IV drug users.
There is not sufficient blood exchange in a bicycle accident to cause transmission. The ONLY way transmission would happen in an accident is if there were massive trauma wounds, to both parties, that required immediate life-saving medical intervention. Your bicycle scenario is not even close to that.
I mean if open wounds are rubbed into each other? Is still no risk?