In my experience, StaBil brand fuel stabilizer will keep gasoline fresh for months and months. I've run gas in my lawn mower (without any issue whatsoever) that had been treated with Stabil and sat in my shed for over a year. I could tell the mower seemed to run a little rough when the gas reached the two year mark.
Stabil will not, to my knowledge, affect the way the bike runs or the way the fuel burns at all. Just follow the directions on the package.
An oily rag stuffed in the exhaust and air intake will keep critters out, and also cut down on condensation.