Let's set the scene:
The horizontal surfaces of the bathtub in my apartment are flat. We have a double shower curtain (with the waterproof bit that hangs on the inside of the tub and the fabric bit that hangs on the outside of the tub) and are careful not to splash too much, but the flat top bits of the tub still get water on them when you reach for stuff. The floor in the bathroom is very slightly slanted, so the open side of the bathtub is slightly lower than the wall side of the bathtub. This means that any water that gets dripped onto the short end of the tub (the side with the showerhead) drips down to the floor, and then slowly flows across the bathroom floor to the opposite wall.
We rent this apartment, so replacing or making major upgrades to the tub is not really an option. (We will have trouble convincing the management company that a few drops of water on the floor merit remodeling the bathroom, since there's no actual leak involved here.)
I need a way to catch the water that wants to drip off the edge of the bathtub and redirect it back down into the tub. (My current plan is to use some foam tubing and rubber sheeting to create a sort of ramp... thing... around the corner of the tub, but I bet this community can generate some ideas that will both look and work much better.)
Additional info: Turns out I'm sort of a natural at drawing bathtubs. A diagram, in case you're confused by my description: