I would get a green Scotch Brite pad and scrub the bit of rust off and put some PB Blaster on the rusted areas. It's pretty much frame saver, but much much cheaper.

I coated PB Blaster on a bare 1950s Schwinn cruiser and let it sit in the sun for a while so it wouldn't leave a residue like WD40 or boiled linseed oil. When I left it in the rain, no rust spots. I usually rewipe it down with PB Blaster once or twice a month.