When I belonged to AAA in Texas, my road service policy included my bikes. The written policy had lots of "fine print". They agreed to send someone out to attempt to fix the bike and agreed to transport me and the bike up to "X" number of miles for free. The "X" miles was kinda short, maybe ten miles. But, here in Houston, I am always within five miles of a bike shop, so that policy would have worked well here.
A friend of mine discovered that "Yellow Cab" in Houston has vans large enough for wheelchairs and bikes, and such. When he has gotten trapped in a storm or has a serious mechanical problem, he has Yellow Cab take him to the nearest coffee shop or bike shop. Usually, under ten bucks...a bit cheaper than joining AAA.