I have small white bumps on my gums that have been around for awhile, 2+ months. I had HPV shots and got new front teeth, moving my bite?

Needs an exam. The three things you mentioned may or may not be related to each other, and to really answer your question you will need to see the dentist that treated you, or another dentist who would needs records from your previous dentist.
Connection. What's the connection between the white bumps, the new front teeth, and your bite moving? I think you really have to return to the dentist that treated you for comparison of today's "bite" to your baseline, and for evaluation of the "bumps.".