How do you clean an old bathtub?

if it's a porcelain / cast iron tub the finish on the porcelain has been compromised thru the years of scrubbing with an abrasive cleanser; your best bet is to have it PROFESSIONALLY restored by a company that refinishes cast iron tubs/sinks . https://www.thisoldhouse.com/how-to/refinish-your-cast-iron-tub

VB,

There comes a time sometimes when you have to accept that Clean and Clean Looking are not the same thing. And if you have an older bathtub, you just may have to accept it as it is or be prepared to replace it. If you are good at home repairs and have friends with the same talent, you can probably do this yourself.

If you want to have this done, be prepared to spend good money and make sure you hire a reputable company and have the parameters of the work to be done clearly stated in writing...and you are given a copy. Be careful about putting out money up front.

There are a lot of SCAMMERS out there posing as Handy Men!

If you have to live with this for now, google some bathroom ideas and spruce up the rest of the bathroom...i.e., paint the vanity, put up new light fixtures, new mirror, new faucet at sink, add some shelves, and declutter. A shelf over the top of the door is a great storage place. Use baskets to hold items and free up space under the vanity.

I agree with all previous responses. Unknowingly, after years or decades of incessant unnecessary scrubbing with the incorrect cleaning products have scrubbed off the original finish. If you decide to have professionally reglazed, here is how to hire a contractor.

https://www.consumer.ftc.gov/articles/0242-hiring-contractor