Or not ride in wilderness areas where riding is not allowed.

I'm all for opening up more trails and areas to bikes, but I think the unfortunate problem to riding in restricted areas is that it could result in limiting new access or even closing off existing trails because the people who don't like bikes could use it as examples that cyclists are not responsible. I also think there are some areas where riding could cause damage to the environment by destroying native plants or making erosion problems.

If the OP needs to walk through a wilderness area to get from one allowed riding spot to another, I would call whoever manages that particular spot and ask them. Then make sure you actually walk the bike through, hang your helmet and gloves off the bars so it's clear you are not riding.