I have been given a second hand bath screen. It's the same style as this:
but 8mm not 6.
It's very heavy, and it's supposed to go on a stud wall. We plan to build the wall using 2x3 studs, but use a 2x4 stud where the bath screen will be to take the extra weight. Will that be safe to mount the screen or do I need to do something else?
Bath screens like this are a dead weight when you lift them but I wouldn't bother using a larger piece of timber. The piece you fix onto the wall will only be held up by 3 or 4 screws anyway by design.
By the time you've boarded and tiled you'll have a fairly substantial wall to which to fix it. You'll be fine.