When replacing a towel bar or other ceramic fixture that fell off the wall due to abuse or poor installation simply remove all the old setting material and reuse the existing hole.
How to repair drywall from ceramic towel bar.
Remove the old or broken towel bar from your wall.
No mess no paint.
How to repair a hole in drywall and install a towel bar on same place.
So lets watch how to do it.
Use a cordless drill and make the existing holes in the wall larger so you can put in toggle bolts.
Put the toggle bolts on the towel bar mounting hardware by sliding the screw into the mounting hole and threading the spring loaded piece onto the other side.