First of all, you can still contract HPV (which can lead to cervical cancer if cell counts turn mutate and turn abnormal in the cervix) despite having received the Gardasil shots. Gardasil only protects you against 4 common strains (Types 6, 11, 16, and 1

. Secondly, I highly doubt a bit of blood is a result of an STD unless there're other side effects that correlate with and STD. Blood after sex can be a result of several things. 1) Check you partner's nails for sharp/jagged edges if you bleed from fingering. A tiny hang nail can create a tiny tear in the vaginal walls and cause a bit of bleeding. It's nothing to worry about though (vaginal tissues often tear microscopically during intercourse and is not even noticed) unless the blood flow does not cease. 2) If you're using NuvaRing as a form of birth control, the friction and close contact of the ring to the cervix can cause spotting and bleeding during/after intercourse. I wouldn't worry or seek help for this though unless it becomes painful or again, the bleeding does not cease. 3) You may just be having "rough" sex and, like possible tears created from a hang nail, your vaginal tissue may have torn a bit in several tiny places.
If you ever experience pain or intense cramping WITH the bleeding after sex though, I suggest you seek guidance from a gynecologist as it could be a result of something more.