+1 on toggle bolt.
However, if you really want to fix the **** out of it, cut out the sheetrock, put 2x4 blocking between the studs at the towel bar height, put a new piece of sheetrock in, tape, float, texture, and paint. You could almost do pull ups on it.
ETA I did this when we moved into our house because the previous owner precariously attached a sink/cabinet to the wall and couldn't find a stud to do it with. The way the sink and cabinet are made, the sink would pull off and fall over if not anchored to the wall. I cut out a 1'x2' section of drywall, added a 2x6 between the studs, and haired taped, floated, textured, and painted the patch. It was surprisingly easy and I've been doing my own drywall ever since. If you have no experience, don't let it scare you.