Make the most of vacation times together. When your doc date can truly get away from hospital or medical practice and not be on call or even responsible for giving advice, it's usually vacation time. Plan to get away from your usual place and travel so that you can have him or her all to yourself. Go interstate or overseas and stay disconnected from the usual day-do-day routines. This will give both of you plenty of opportunity to spend quality time alone and to learn a lot more about each other.
Naturally, as with any date, don't be pushy about going somewhere. Raise it as an option to see if your doc date would like to go somewhere together during his or her vacation.
Be prepared for the possibility of a volunteering holiday somewhere challenging. If your doc date loves volunteering, you may need to hop on board and pitch in too. It's more fun when you're both involved.