I don't dive nearly as often as I would like and I recently (last October) did a week on a LOB out of Nassau (the Aquacat). I flew down a couple days early and dove with Stuart Cove for a 2 tank afternoon dive to knock a little of the rust off prior to doing the LOB. If you are planning on diving with Stuart Cove, the advantage of doing it prior to the LOB is that it forces you to travel a few days earlier and then if the airline sends your luggage to Nashville instead of Nassau, you have a built in buffer for them to find and return your luggage before you get on the LOB.
Depending on which LOB you are doing, you will likely get between 19 and 25 dives in during the week (some don't do night dives). You will probably see sharks on a couple days, but you will probably not be "totally sharked out". On my last trip, we saw reef sharks at the Austin Smith Wreck and at Split Coral Head, and a few random nurse sharks, but that was pretty much it. Keep in mind though that this is the ocean, not an aquarium and YMMV.