The solution to your problem is dependent on the level of cleanliness you require and on your hair style. Fact is, if you are trying to clip your hair in a contemporary residential bathroom there is no solution that will prevent hair bits from winding up somewhere. The best you can do is maximally contain what you can with the expectation that you'll be doing some cleanup. With that said I recommend making sure everything is dry when you start. Dry dry dry. And don't get anything wet until you are 100% done. Use the towel, or sheet, or newspaper as you see fit. Then vacuum.
Here is how I do it which keeps the hair out of the bathroom: first I clip my hair with my head in a laundry sink. That's in the sink. I bend over the sink and clip my hair. When I'm done with that stage I take my close-trimmer and a mirror to clean up the back. I currently do this in my dog's kennel area. I've done it in garages, basements, back porches, anywhere but inside. I've gotten really adept and trimming the back of my head.
Once I'm done I go back to the laundry sink and scoop the hair bits out and throw them away. I clean it up by washing the few leftover bits down the drain. I've never had a drain problem. Then I sweep the floor in the kennel area. Then I take allot my clothes off and brush myself off very very well and then get in the shower. When I get in the shower I sit on the floor. I do this so that when the water hits my head the heat that bounces off stays contained at the bottom of the shower. If I stand up hair bits get scattered far afield.
This is how I keep the hair out of my bathroom. I recommend that you stand in your bathtub. You will need a mirror that you can suction cup to the wall and a hand mirror. But seriously, if you have hair all over the floor of your tub it will be a task to get it down the drain. And it will be stuck in crevices in the shower curtain or other places.