How the captain is addressed, based on the various series we have available, is dependent on your relationship with said captain.
As you said, Bones and Kirk have an informal relationship.
Most captains in the Star Trek franchise (who are a main character) have at least one member of the crew they are particularly close to, usually due to a prior relationship. This is good for storytelling.
Picard has Beverly Crusher, who is indeed his Chief Medical Officer. She regularly uses his first name, and he reciprocates.
Sisko has Jadzia Dax, who regularly calls him Ben or Benjamin, but she is not his CMO.
Janeway has Tuvok, who I don't recall ever addressing her informally, but Chakotay does on quite a few occasions. Note, not all first officers are in the habit of doing this, with Riker very rarely using Picard's first name for example. I think Chakotay is supposed to be closer to Janeway due to their isolation as commanding officers far away from the rest of Starfleet. Back to the point: neither Janeway or Sisko's CMOs have a regular tendency to use their captains' first names.
Captain Archer has this closer than usual relationship with his first officer, who doesn't often use his first name, but neither does his CMO.
To summarise: Some characters have a close, somewhat less formal relationship with their captain (to a point) and are on first-name terms. This appears to be the Chief Medical Officer on more than one occasion but it does not seem that there is any regulation that accounts for this. Indeed, some doctors would appear somewhat out of character in treating their captain informally in my opinion.
Note: The Starfleet CMO has some intruiging rights and responsibilities, such as the ability to relieve the captain of duty in extreme conditions, but this does not mean that they out rank him/her. Saying that, I'm sure they can address the captain however that captain feels comfortable during intimate medical procedures!