Occasionally, I have to account for rust in stress calculations. It's necessary to reduce the as-designed thickness of the part and see how much material will be left over after a period of time. Here's what General Dynamics Electric Boat has to say:

Corrosion allowances may be necessary for some calculations. Recommended corrosion allowances for items wetted by seawater are:

Nonferrous Materials 0.050 inch
Ferrous Materials 0.065 inch
Copper Nickel 0.050 inch

Double these values if in contact with seawater on both sides. This corrosion allowance shall not be considered as contributing to strength

Of course, we are talking about ferrous materials; materials containing significant amounts of iron. As Catatonic wrote, surface rust is not a problem. Sand to bare metal and prime and paint.

If you are talking about a 1" plate, the corrosion allowances given above are neglegible. For the thickness of tubing used in a bike frame, however, they are very significant!

I'll spare you the gory metallurgical details, but the method of welding can contribute to corrosion. The heat of welding affects the metal as it cools, and can make the weld or adjacent material more prone to corrosion. This is especially true with "stainless" steel. I'm guessing a cheap bike was simply welded and allowed to cool. Not the best senario.

Brazing temperatures are not as hot and will not contribute to corrosion the way welding can.

If there is excessive pitting, you may consider ditching the frame.

If you have a photo, we may be able to give you better advice.