As chief medical officer, McCoy might be required to monitor the bridge crew during various situations and then file his evaluations to Starfleet.
I actually think it's good that McCoy isn't in sickbay all the time because it suggests that he isn't the only doctor onboard, even if we don't see the other ones. I doubt that sickbay is only open when the CMO is there.
Plus, he's McCoy
--he can go anywhere on the ship he wants. But when there's something big going down, you bet you'll find him in sickbay.