I would suggest showing up in person. You bring a smile and a face when you show up, vs talk to someone on the phone. Dress professionally and bring a resume, business card. Don't expect to talk to the doctor the first time you visit. Drop off your resume, and business card, and let them know that you're interested in shadowing Dr. X. The receptionist will most likely take your info, ask what hours you're interested in, and then they'll call you back later. Don't take it personally, but the dentist is most likely busy at the time... if they don't call you back in a week, I'd say check back again (this time by phone).
I once went to my orthodontist to ask to shadow or volunteer, and they ended up referring me over to the general dentist next door who had just bought the practice. I dropped off my info and met the dentist later for an interview... got the job... it was minimum wage, but an AWESOME experience that I still reference to when people ask me when I became pre-dental.