I had a similar dilema...just nowhere to put them and I do not like towels touching each other as they won't dry.
So this was my solution after a month of trying everywhere else. Backside of the bathroom door.
The bottom towel bar had to be mounted first on to a piece of oak hobby board from Lowes because everyone wanted to use it as a handle and those doors are too thin of cheapo wood it kept ripping out. SO I mounted it to the oak then used six screws to mount it to the door. Not coming off now.
The top bar is no problem as no one grabs like a handle.
Of course my wife will notice the towels are not hanging perfectly in the pic but...oh well..
Also when we shower we open the bathroom door and the towels are right there when we get out of the shower...but works in our CKTS...may not in others,