lillo:

Who says you need mechanical fasteners? Clean the fiberglas and the back of the bracket, apply 100% silicone and tape it in place for a day or so. Carefully cut off the squeeze-out with a razor knife after its set up. If there is enough footprint on the bracket, this may work.

You also might be able to use 3M VHB tape!

Would these methods be sturdy enough to hold the bar ? taking in consideration that there will be some pull up and down on it to move the position of the shower head .

Worth a shot before you screw the surround. If you have to screw thru the surround you will need to have the screw into a stud or blocking (which should have been figured in the original layout).

lillo:

Have a local solid surface fabricator fabricate a color matched piece 2" longer than the bar you want to mount. Drill through the solid surface completely to mount your hardware (don't screw directly into the solid surface), making sure the back is flush. Silicone the solid surface to the shower wall. It ain't comin' off, even if you used it as a grab bar.

Thank you for your suggestions . I'll give it a try with the silicone first . If it doesn't work , I'll the idea of adding the solid surface .