Vinegar is sometimes used to remove rust from things, but not the way you tried to do it. I've seen it used in removing encrusted rust from steel or cast iron tools. In that case the tool is immersed in vinegar solution (citric acid also works). When the part comes out of the bath, it is immediately rinsed, thoroughly dried, and often a rust preventer is applied.

I would lightly sand to remove the new oxidation. (By the way, rust is a type of oxidation.) You should be aware that recently cleaned bare steel can rust again pretty quickly, especially if it is at all humid where the part is located. You will probably want to move onto the next step promptly.

I'm not an expert on bike painting, so I'll sign off here....