Couple of random thoughts.
First, I can't stand the big tourist islands of the Bahamas. Nassau and Freeport are gross and outside the resorts, crime is an issue. It's not a war zone, but still.
I do like the Abaco Beach Resort and Marina, but it could add up a bit during the prime season. It is very inexpensive off season, there is also nearly no one there. Been there, done that, not with my boat. People routinely come and live on their boats, though rarely for more than a month or two.
I can't recall how long you are permitted to stay in the Bahamas. Look it up, but I think its 6 months. One thing is for sure, the Bahamas do not want anyone other than a citizen working there, with few exceptions. I understand you will be working on the internet, but I would keep that entirely to myself!
Finally, I do agree with a poster above, the Virgin Islands would be far superior cruising grounds. Most will point to shallow waters as the prime issue for cruising the Bahamas, but I think that is manageable. The much larger issue is that once you're on a given island, there isn't really anywhere to day sail. The BVIs and USVIs always have an anchorage on another island that can be reached in a couple of hours. Sometimes less.