I volunteer making houses more functional for elderly homeowners to live in them. Age in place. We fix up one house each spring. Anyway, one of the things we do is put tons of grab bars in the bathrooms. There is a towel rack you can buy that is actually a grab bar. It comes with massive anchor bolts and is made of very sturdy material. It's a great idea. Seems to me that all towel bars should be made that way. Elderly people aren't the only ones who could use them. The towel racks in our bathroom are a little loose from people grabbing them.
Attach the screws to a stud, or use something like
wingits, and you can do chin ups from that bar. If you're short enough.