The diving bell first becomes available after Sequence 6, Memory 1, "Diving for Medicines." Thereafter it becomes available for sale as a ship upgrade for 5,000R.
Note that you don't have to actually fully plunder all wrecks, you merely have to put the diving bell in the water at each.
Each wreck and its corresponding location follow (credit to www.vgfaq.com):
Ambergris Key 55, 178
Anotto Bay 621, 277Antocha
Shipwreck 630, 660
Devil's Eye Caverns 487, 357
Jiguey 565, 539
Kabah Ruins 769, 145La Concepcion
Shipwreck 186, 296
Petite Caverne 901, 264San Ignacio
Wreck 378, 769
San Juan 479, 487
The Black Trench 215, 449
The Blue Hole 471, 170
Segmentnext.com has a detailed written walkthrough of each of these locations here:http://segmentnext.com/2013/10/31/assassins-creed-4-black-fl...
Below are video solutions for all shipwreck locations (credit to VGFAQ and AFGuidesHD).