Eastwood and several other companies sell rust converting primers for the auto restoration trade. Several of the products come with extension tubes that allow you to fog the product into enclosed areas and work well for bike frames. Use your rust remover of choice and rinse with water. Give the frame a final rinse with Prep Sol or other appropriate solvent/cleaner and take it out in the sun, tipping it in various directions to make sure that all the solvent has drained or evaporated. Protect the outside of the frame and any threaded areas with masking tape and/or other products designed for use with automotive primers and paint. Fog the rust converting primer into all the tubes through any opening. Try not to get much in the area where the seat post will dwell as it can cause a tight fit. Do this in a few lighter applications so you don't have primer running down the tubes and puddling. Tip and rotate the frame for a few minutes after each application to assure that no primer pools anywhere. Allow to dry overnight or longer before reassembling. The rust converting primer will make any specks of rust left behind by the rust remover chemically inert.