For light surface rust, visit the grocer. Over in housewares, get a COPPER Chore-Boy pot scrubber pad. Copper is softer than the steel of the barrel.
Wet the pad with oil (Kroil or Sili Kroil is great, but if you don't have it, any light oil). Change to a clean spot every so often- the rust loading up on the pad is abrasive itself.
When you finish, gun may have a coppery look. Clean soft cloth, Hoppes #9. that will go away. Change to clean spot on cloth now and again.
Be sure to oil it after you finish. CLP is good stuff (cleaner/lube/ protectant- NOT the chemical calcium/lime/rust remover- CLR) THAT will strip bluing off- its 20% lactic acid.