If only the skin is damaged without bleeding, can the virus enter the body for blood exchange？
The only ways people get HIV are to have unprotected vaginal or anal intercourse with penetration or to share INJECTIBLE needles that they inject with. This is very different than a needle stick which will not transmit the virus. A needle poke would be something that was exposed to air and therefore, all virus is dead. Furthermore, this doesn't happen. How would a syringe be on a bike that you didn't see? Think about that. Your anxiety is running away from you. No risk but also most certainly never happened.
I would class this as a "never event" as it wouldn't really happen in the real world. Lets point out individual things....
1) Syringes with needles are just too long to fit inside a bike saddle.
2) Even if it did, the syringe would need to be plunged.
3) Even if it was plunged the vast majority of people do not have HIV.
4) If it wasn't plunged the statistical rate of getting a HIV infection if it was positive would be around 0.03%.
5) Point 1 and 2 would not happen. It just wouldnt.
So no risk at all.