Bath with sliding door..

Not sure how to do this. I am redoing the bathroom, moving a small spa bath along a wall that has a sliding door. I have a piccie of it, but it may not have loaded..... We want the bath as close as possible to the wall to save floor space.
The sliding door frame has a horizontal in about the right height, but I don't think that the frame is strong enough to be a reliable support for that corner of the bath and the spa pipes will prevent me from heading too far under the bath edge for a support I think. I think that I have not much over 40mm max.

other question, do I leave the studs open behind the bath?