Most folks heading to or from Grand Bahama stage from the Lake Worth area. in order not to fight the Stream. This will mean additional time for you to bring your boat back to Miami, assuming that's where you dock it.
There are several marinas in the Port Lucaya area. I have not personally stayed at any of them, but I read a good review on the Port Lucaya Marina not to long ago. Regardless, chose a marina close to the Marketplace as you'll be spending a lot of time there.
If you choose to return to Bimini and would like a sheltered place to anchor out if wind is out of N,E, or SE, try the bay between North and South Cat Cays. You'll probably have the place to yourself. Great beach combing along South Cat Cay as it's deserted and is not frequently visited.
Hope this helps.