Close...they make even smaller bottles for tub/tile.

I used these to cover rust spots in a shower and sink once. It acts like a new layer of hard tile. If you don't care about appearance, this is a good choice.

Cover the rust in this stuff, let it cure. Then add the caulk over it.

https://www.amazon.com/Rust-Oleum-244166-Specialty-Touch-White/dp/B006ZHVLYG/

*Edit: if it's a small area, a few inches wide or so, these should be enough to cover it with two layers. It goes on a bit thin, so i'd recommend two layers.