Most of my work is spindle turning as opposed to bowls.
I have found more or most water leaks from the end grain, any wet turning I do turned near the finished diameter allowing for remounting then stand on a wooden floor and let it drain naturally gives me best results.
Other shapes, I have a dustbin outside full of wood shavings and bury them in it, it has a loose fitting lid so moisture can get in and out without being soaked.
I don't do any large pieces wet, like you can't be arsed with all the agro.