How can I mitigate the risk of public urination charges on long rides?
Plan your route accordingly.  Make sure there's a couple gas stations or restaurants along the way that you could stop at if the need arises. It's probably a good idea to be somewhat close to civilization not only for urination purposes, but also in case you have some major mechanical problem with your bike, or you fall and get hurt.  This doesn't mean your route has to be urban, but you should be able to plan a route such that you pass by some kind of civilization every 40-60 minutes.  Alas, if you are that far out, you could always go off a side road or into the bush and relieve yourself there.  If you're so far from civilization that you can't make it to a gas station, odds are that there won't be many cops around to prosecute you either.