Cleaning my bathtub

I am trying to get the bottom of my bathtub white. I cant tell what it's made out of, but its almost definitely some kind of plastic, like acrylic or fiberglass. For the sake of not ruining it because we're renting, I'm gonna assume its fiberglass because I believe thats the more fragile of the 2.

I cleaned it recently with a scrub brush, and a solution made of water, vinegar and dawn dish soap. It got rid of the nasty orange coating that likes to grow, but the grey staining on the textured bottom is still there no matter how hard I scrub. I dont know what it is or how to get rid of it. When I lived with my dad the same grey staining was there, and I ended up using a drill brush to get rid of it, but looking back on it, that was probably very abrasive and I dont want to damage our rental tub with a drill brush (and we dont have a drill anyway).

What cleaners should I use to clean my tub? I keep seeing different suggestions. I just want to make it white without causing damage.