This is a simple solution for removing small debris from the bottom of your hot tub. Buy a Super Squirter water gun from the dollar store. This is the kind that acts like a piston inside a cylinder. Pull up the piston and it sucks in a lot of water. Push on the piston and it squirts it out.
The tip of the water gun has a small hole. Use an exacto knife or fine tooth saw to cut a 20 degree angle across the tip, enlarging the hole.
To use, simply position the tip over the dirt in your tub and pull up on the piston. The dirt will be sucked in and you can eject it over the side of the hot tub. Problem solved!