Also, some small airports will have plain pure gas ( I think the term commonly used is AVGAS, and it is not really different than what we use in our vehicles, except it is exempt from the federal additive guidelines.)
Airport "avgas" for piston engines is 100LL, which is one hundred octane low lead. It is low lead compared to older avgas formulas, but it still has four times as much lead as leaded auto fuel ever had. A dose of it every now and then wouldn't hurt your bike, and storing the bike with some 100LL would be good (100LL is very stable), but I wouldn't run a lot of it or over awhile you would risk fouling plugs, rings etc.. Besides, it costs about $5/gal right now, who can afford that? ($5.35/gal at my local airport right now, but other airports near here have avgas for $4.50/gal)
There are some airports that carry "autogas" for those airplanes that are certified to burn it. It usually is just unleaded regular with NO alcohol. Unfortunately it is very rare for an airport to carry autogas since they typically don't want to deal with the tankage, the affinity of autogas for water, and the liability (as advised by my FBO when I asked if he would ever sell autogas). If you can find an airport that carries autogas it will typically cost somewhere in the middle between street gas and avgas, sometimes closer to avgas.
I can still buy unleaded regular and premium with no alcohol at my local convenience stores/gas stations (I pay more for it though), so any engine of mine that may sit unused for bit will be fueled with it and I also carry it in cans to the airport to put in my airplane. If it is going into a vehicle that I am driving a lot then I will usually just put in whatever gas is cheapest and that would be from the regular pump with 10% alcohol.
Go to pure-gas.org to find local stations without alcohol, there may be one close to you.