I’ll go first. After your turn the water off in the shower but before you get out, use your hands to wipe off any standing water on your body. Maybe even give your legs a bit of a shake. This way, you won’t drip nearly as much when you get out, keeping the floor and your towel drier.
If you shower at the gym, you don’t need a whole bath towel to dry yourself. A regular hand towel is sufficient, and it takes up way less room in your gym bag.
Bonus points for those really thin microfiber types. You wring them out as you go to get the majority of water off your body, the rest air dried quite quickly after that.