In all the tubs in my house I use a little drain cover that either clicks in place or screws in place. It lets water out through tiny holes but hair mats on top so youhave to clean it out every use.

I've used this to successfully declog hair in a sink. It is cheap but beware even though it is plastic, it is sharp.

Try this: zip-it-bath-and-sink-hair-snare

I haven't used these but they may be helpful, also.