I like Richard's idea also with a couple caveats. First of all those resorts all charge PP since they're waterfront. And most/all have a single supplement if you are one. The Hamlet Oasis (or Coral Paradise) condos aren't waterfront but rent by the condo afaik not per guest. CP seems to be a less expensive option there. Due to location you can walk to Dive Friends/Hamlet or Habitat for boat dives. Either end of the Cliff dive site basically.
Also look for Sand Dollar condos on vrbo.com. Some of the privately owned units rent there for less than going thru Sand Dollars rental agent. Since a fuss a few years ago with Bonaire Dive/Adventure over dock usage, the Dive Friends at Sand Dollar (shop is streetside for easy tank pickup - has built a tank shack and steps down to the beach for their guests on the far south end of the property which is the middle of Bari Reef.
Den Laman condos is nice but more upscale, a lot newer and pricier. I believe all the studios face the parking lot also.
Bari has one of the largest fish species counts of any reef in the Caribbean - largely due to the REEF surveys done there by guests with the BD&A naturalists - they have a fish ID/count dive option. My buddy did it, he counted 185 species and his count was sent in to REEF - one dive. It's even sort of fun there in the shallows to the south - there's some coral rubble, hurricane rubble in 10' that's fun to poke thru. I filmed a Batfish there although I didn't know what it was till reviewing video with the naturalist - he said it's pretty rare to see one there.
Check out Black Durgon Inn also - they match your requirements almost exactly. It's a smaller property, has a "community" kitchen and happen to be the best shore access to Small Wall? afaik.
http://www.blackdurgon.com/
Just past Bari Reef to the south (past the Coco Beach club) is Eden Beach. They do have some smaller units - IDK about pricing. Spice Beach Club is on-site - a reworking of their bar/restaurant area and the main Wannadive shop is there. I've seen divers shore dive there but IDK what site/how good it is.
Coco Palm Garden/Casa Oleander mentioned above is more affordable but across the street from the water in Belnem south of town. I believe they're near Bachelors Beach which probably makes Buddy Dive at Belmar condos your closest shop location.
We've stayed at Belmar - there you would have 24/7 tank access since your condo key gets you into the public areas of Buddy's for tanks, Nitrox analyzer and the upstairs units have lockers there also. Plus wetsuit storage. I'm sure there's some single bedroom units there but it will be
pricier since all have full kitchens, patios etc. - and it's a newer more upscale property than the original Buddy Dive location. You also get use of the Buddy Drive-thru when diving north.
There's no food options in Belnem (except Hotel Roomer's small restaurant) so everything is a 5min. drive to town. The two main markets, Van der Tweel or Warehouse Foods - are a pretty short drive away as they're on the east side of town.
One last option, check out Carib Inn on the south end of town. I'm sure there's a dive there but IDK how good it is. I believe they still rent by the room not PP and have smaller boat(s). It's a little south of the Divi and people walk to restaurants in town from there so maybe a block or two more.
The best 24/7 access has to be Goood Dive in town now since they have an outside fill station. It's just not an overly convenient location. Most of the apts. etc. in town are across the street from the water and with the piers etc (Town Pier is the cruise pier) there's really only 3-4 dive spots. The Divi Flamingo is a little south of town but their shallow reef was pretty torn up some years ago so IDK how good it is now. Afaik, your locker (and tanks?) are on the dock.
Some of the Dive Friends post mention a tank locker - apparently you can call and ask tanks to be put in it for overnight use. IDK the details. Someone also recently mentioned that Habitat stages Nitrox tanks "upstairs" now. Nice to not have to walk them up the ramp from the dive dock area.