What I did was email many of the local dentists. I live in huge city, so there were plenty to email. I emailed 20+. However, out of all the ones I emailed, only 2 emailed back... one of which said I can't because of patient-doctor confidentiality. And the other dentist let me shadow 🙂
But what I found to work best is to ask your general/family dentist since you're the patient and you give him/her business. I also did this method and it seems they can't really turn you down. If you have a good relationship with your general/family dentist, it will be more beneficial to shadow him/her than a stranger dentist since he/she can probably also write you an excellent LOR. Good luck! 🙂