Honestly, law abiding folks tend to overthink this stuff. Criminals walk around illegally armed all the time and rarely does it become an issue. Just follow the law (FOPA) and don't do anything stupid (gun related stuff out of sights, don't speed, etc), and you'll be fine. I've FOPA-ed on a number of occasions through several different states and never even got pulled over, never mind had my car searched.
I drove through Maryland recently with my girlfriend and told her about the Florida couple that got harassed there once. My lady was offended that I would tell her this story because "do you think I'm that dumb" to answer any gun questions