Spray a basic bathroom cleaner all over the interior of the tub. Let it sit for five minutes, but don't allow it to dry.
Scrub the walls of your tub with your brush, starting at the top and working your way to the bottom. Rinse the brush in the sink every few minutes.
Scrub the base of the tub interior with the brush. Turn on the shower to rinse all the loosened dirt down the drain.
Spray the non-slip coating with the cleaner again. Let it sit for another five minutes.
Scour the non-slip coating with your brush. Move it in small circles to break up the grime. Rinse it away with the shower.
Pour a small amount of acidic surface cleaner on your sponge or directly on the non-slip coating. Look for one especially made for bathtubs or bathroom cleaning.
Wipe the acidic cleaner into the non-slip coating until all the remaining dirt is gone.
Rinse the tub.