Whenever I have rust that I need to remove, I like to use a rust remover product. Some examples are CLR and rust away. YOu can buy these in the regular cleaning section of any major store. Just spray on the rust, leave for a minute, and scrub off.
Duro Extend will bond with the rust (no scraping) and produce carbon steel. It's black but then the color of rust has never been a fashion statement. Follow directions.
If you are prepared to spend a few hundred dollars, you can hire a company to refinish the tub. They come in and spray a coating that lasts several years. If you are looking for a DIY project at a much lower cost, you can buy a bathtub refinishing kit that contains a strong enamel and apply it yourself.