My university's dental school gave my university's undergrad. a list of dental school alumni who
wanted our undergrads to come and shadow them. They made us promise to keep the list private and only for our university. If your uni has a dental school, maybe consider giving that a shot? Big thing I learned from this though: a connection with the dentist helps a lot. Before you go call the dentist's office, research his/her website and see what school they attended, if they're big on some CE stuff what they did, etc. etc. Then, when you call, express this special interest as part of the reason you want to shadow with them.
Example:
Receptionist: "Good Morning, Dr. X's Office this is Y speaking, how may I help you?"
You: "Hello Ms. Y, How are you doing?"
Receptionist: "Pretty good and yourself?"
You: "Great thank you. I am calling because I am a pre-dental undergraduate student at [insert your school name], and I am very interested in Dr. X's work in [insert field of expertise]/his experience at [insert school name]. Do you think it would be possible for me to spend some time shadowing with the office and getting to learn about his experiences?"
This method of asking shows the receptionist that you respect them enough to have done your homework and that you have a genuine interest. After this, luck is a big factor.
A few more ideas:
1) Try community health centers/public clinics/free clinics. These clinics are much more informal- you can wander between ops if you want, and they often have certain days where they have specialists come in. I love spending time in these clinics b/c it lets me pop in and out of rooms and speak to as many different staff members as possible. I've gotten to talk to/observe dental students, endo, general dentists, CHC managers, just to name a few.
2)
@ajj70 proposed a good idea- Ask your own dentist, and if s/he can't do it, ask for a reference to another dentist.
3) make an individualized request to each practice- see above.
4) Don't give up- Even though I had a list of practitioners who were willing to let undergrads from their alma mater shadow them, I still had 3-4 no-go's. But that moment when you hear that first "yes, we can set something up"- that's such a happy moment. Keep trying.
5) Ask your pre-dental advisors/clubs where they got their shadowing done.