Although most call them a "bladder tank" They really are not. They are merely a tank large enough to hold 10-15 gallon more water than your tray will need to be concidered full.
Most setups use fairly large inlet/drain back in the bottom of the tray so filling & then draining of the water is fairly rapid.
A valving of some sort, you choose whether simple ball or solenoid valve(s) operated from Mach, is arranged to apply air pressure ( usually not very high pressure) to your "bladder" & force the water up into your tray. When finished cutting release air & allow water to gravity drain back into the tank.
If this isn't enough information let me know & I'll hand draw you a rough sketch of my idea(s) for a water tray & post it up in the next couple days.
99% of what I cut is Ox/Fuel & heavier materials as I stated above. Below is a pic of the small drops & swarf of about 1 1/2 weeks of cutting. I really wouldn't want to have the job of cleaning all this muck from a water table.
My slats are a mere 3" on centers. & still loads of slugs & all the "blow" end up here.
Oxy/Fuel doesn't create near the smoke/fumes as plasma however. My shop is well vented so fumes from the Oxy isn't bad at all.
The pic really doesn't show the volume of crap in the catch trays. That muck is around 3" deep right now. I lift the 2 trays out with my fork lift & dump them in the scrap hopper as needed.