Use vinegar or citric acid (lemon juice) to stabilize the rust, then a cloth to rub off whatever it will.

Repeat and rinse well, and paper towel dry. Now paint or clearcoat to seal. If you don't see much weather, multiple coats of wax be adequate protection.

FWIW the steels typically used for bikes, especially better ones, don't tend to rust that quickly, except, maybe, in harsh marine environments. All my steel bikes have seen years of hard all weather use, and never more than a vinegar wipe every once in a long while and never did worse than show their age.