Potentially, IF it would have been malpractice  (or neglient; that is, unreasonably careless) to drill into the existing bridge, the dentist who did it might be liable for the cost to correct the situation and for any extended pain, etc. you suffered. If the out-of-pocket (not paid by your insurance) cost to you is $3,000 or more, its probably worthwhile to retain an  attorney and let the attorney seek compensation. For less than that, you  may wish to try the demand letter; if the dentist does not pay something, you can then decide if you are willing to try suing in small claims court, acting as your own lawyer (pro se)--though be aware, you'd need expert dental testimony (e.g. from the new dentist) to prove your case, which could cost more than you hope to recover.