Floors would work as well but take far longer to build and then demolish.
Also might leave awkward submerged ex-floor materials, if you can't get in there and clear it out. At least a bridge dismantles to an adjacent walkable edge on the same level.
(Unless you somehow manage to strand it and your building remover on a disconnected side-bit, of course...
When digging a long well-shaft down into the caverns, I usually try to insert a bridge at the top level of the cavern I'm digging into to catch the stone falling down the shaft channels. The alternative is to not save the lowest channelling until you've cleared all the fallen stone off of that spot, and
then breach the floor-thickness final stage without any rock falling into the water below. If that's not possible, due to cavern height at that point, dig into the lowest non-cavern level early on (before being channelled into) deal with the waste rock on that spot how you wish, then channel it, add a bridge or hatch covering, then let the rest of the wellshaft be dug without fear of rock (or miners) falling into the pool, opening/removing the bridge or hatch when all is well. IYSWIM. NPI.
(Not that it causes any problems, saving the loss of the rocks involved which might be valuable ores/fluxes, etc. But if you weren't too bothered about them, the alternate alternative is just to designate hidden and forbidden anything that does find its way into the water, of course.