What are you building the diving bell out of

For example, out of animal skins. This construction is supported by internal pressure, it does not need strength.

More to the point, why would they want to? What would drive them to do so?

Want exactly what? If "smelt metal", then probably the same as humans, accidentally placing copper or tin ore in furnace. If "having underwater furnace" - it is easier to operate than one placed on raft. If "why use fire at all" - to make watertight pottery.