There are also other products you might try. I've had good luck with Jasco Rust converter on old cars etc. Basically it's a phosphoric acid/chromate liquid that converts the rust to iron phosphate. I am currently trying it out on an older Whirlpool outer tub; I'll see how well it works. It appears to etch/haze the porcelain glass surface slightly, but it doesn't destroy it completely. AFter it dries overnight, you're supposed to brush off any white powder and then primer over it. Any oil based primer will do at that point. You don't want to get the Jasco on good paint; it can eat the paint down to the bare metal (depending on the type of paint, it seems). You probably also should wear gloves, although for small jobs I've gotten by without gloves.
I've also had good luck with Rustoleum oil-based Red Primer - it has a lot of fish oil in it, which penetrates the rust, and is very resistant to further rusting. However it's best if this oily primer is left to age or weather for some time before top-coating, because if there is excess oil on its surface it can inhibit adhesion of a top coat.
If it were my tub, I'd treat the rust spots with Jasco and then give them a brush coat of Rustoleum red primer. Since the tub will never be seen again in normal use, I wouldn't bother top coating it, although a coat of oil-based black enamel probably wouldn't hurt, and would look better to a service person... lol...
