You can paint it with a kit. We used RustOleum kit and it has held up for 2 years. Follow directions exactly.
Home Depot and Lowes have bathtub refinishing kits
Rust-Oleum does make a product that is approved for bathtubs.
Please consider looking over these links below and consider the Amazon website which has questions and answers along with reviews which may help you decide is the product is right for you to use. I have use the Rustoleum helpline they are very knowledgeable and educated people that might help answer your questions or concerns before you consider the project.
Here's how I did it: https://bachelorettepadflip.com/2014/07/03/glazed-over/