There are five PADI dive ops in Bocas del Toro. Four of them, Bocas Water Sports (BWS), Dutch Pirate, La Buga and Starfleet are in Bocas Town -- the main town in Bocas del Toro. Starfleet was suspended from PADI last year and recent got its certification back. Even so, after diving with them a few times over the past 12 years, I would not recommend them. La Buga seems to be much more focused on surfing than scuba diving. I haven't dove with Dutch Pirate, but the have a new boat and their shop and rental gear look fairly good. Since 2010, when I come to Bocas, I dive with BWS. Any and all gear that you might need is included in their dive rate, which is very reasonable. I believe a 2-tank dive is $65 ... $55 if you are doing multiple dives. The BWS DMs and Instructors are excellent and, unlike Starfleet, won't cut you short on dive time.
As for staying on Bastimentos. Yes, there is another, much smaller, dive op on Bastimentos. I haven't dove with them, but based on the reviews in Trip Advisor, they seem to do mostly resort-course dives with non-certified divers. Bastimentos has a few very nice beaches, a zipline and a couple of restaurants. (Beware of two things on the beaches: 1) the undertow. Each year, there are two or more tourst fatalities due to very strong undertow, particularly on Red Frog Beach. It's not every day that the undertow is that strong, but there are no life guards or warnings on any of the beaches. 2) the thieves. Never leave anything unguarded on the beach. It will disappear. That goes for everything from wallets to clothes to prescription glasses to well-worn flip-flops. The other very important thing to realize about Bastimentos -- and any of the out islands away from Bocas Town -- is that you will be very isolated from restaurants, bars, scuba shops, etc. You'll have to take a water taxi, which will cost you anywhere from $8 to $20 to get to Bocas Town. And, it's dangerous to be riding in water taxis at night as most boats (including taxis) do not have running lights. There have been crashes and fatalities at night.
Please don't get me wrong -- Bocas del Toro is very unique and beautiful. And, while the water may not have the clarity of Grand Cayman, there is a lot to see and many good dive sites. Bocas Town has a number of very good restaurants, fun bars and good places to stay that are within walking distance of everything. It's worth the trip.
