In this situation, I'd absolutely rent a car instead of using a
DCL bus. You then aren't waiting for a bus, and can get there whenever. You can then pick her up outside the terminal at whatever time she's available, and then drive to a park to have a nice reunion. Then drop her back off when she needs to get back on board, and then you can either (a) drop the car off for a one-way rental or park it in the garage. Depending on the length of the cruise, a week-long rental is cheaper than two one-way rentals (though you must pay to park), and depending on the number of people in your party, can be much cheaper than two one way DCL transfers. (With 4+, a car is MUCH cheaper.)
DCL's busses are timed for embarkation, so chances are that the first busses won't arrive until 10:30-11 am. If she's free at 9 am, you've missed a couple of hours to spend with her...especially if she has to be back on board by noon.
The only reason to take a DCL bus is that you want to dedicate your morning to be on the ship at the earliest possible time. That's not your situation.