I tend to follow the speed limits and obey the traffic laws. I have over 50K miles on the road and have never been pulled over. If I did make a mistake they still have no reason to search me or my vehicle. Yes, I'll take that chance.
When we stop I remove the gun and either take it inside the hotel or store it in a hard saddle bag while eating, shopping, etc. I try to be discrete and, knock on wood, have never had a problem. I won't travel without a gun, period.
Like I said, it works for me. YMMV