Is there a hair trap that you can access from below? It would probably contain the washcloth. There should be some kind of a trap to prevent gases from coming up through the drain. I expect the cloth will be at a turn if not in a trap.
If you have a pop up type of drain it could be caught on the linkage from the tub wall to the drain. You have one of two types of traps on a tub. Either a drum trap -- which would have a removable top to access it, or a running trap which is part of the pipe and would have to be disassembled to check it out -- it would be an actual part of the drain piping. Its possible that it is just stuck in the piping and you would need the snake to try and either retrieve it or force it down the line. You could also try a toilet plunger on the drain but you will need to cover the overflow (where the lever is for the pop up portion of the drain) with a rag for the plunger to work.