Not an expert, but my impression is that the Gall Bladder is little more than a space in the liver where gall accumulates. When people have them removed, bile is still made, tending to accumulate in one place, so whether it 'regenerates' or not, you still can grow new stones.
By the way, there ARE other options for getting rid of/dissolving the stones than having an operation: e.g. to do with diet or ultrasound or (especially) colon flush, which we have found to be very effective.
The first time you have a colon flush, you will probably feel better going to a "hydrotherapist", who will talk you through it, give you a gentle colon massage during the flush and help you get to know your colon.
But when you are used to it, the full colon flush only takes you a bit over an hour if you do it yourself with a special board to lie on at home with music and essential oils to breathe, see https://www.hps-online.com/images/boardontoilet.gif
Alternatively you can just do a coffee 'clyster' (look this word up: its a synonym for a word I'm not allowed to use here!).
You use filter coffee. The method has the advantage of giving you a caffeine shot (caffeine is absorbed in the colon without having to digest the coffee). All you need is a home 'clyster' pouch (look this up, with the normal word, on google) that hangs on a hook near you while sitting normally on the loo, with a personal delivery tube. The whole thing takes as much time as a relaxed number 2 reading a magazine.
There are loads of references to coffee 'clyster' on google - again using the normal word not clyster.