The Federal Height limit on vehicles is 13 feet 6 inches . I don't know what the Federal limit on bridge clearance is but it higher than 13-6! While I've been concerned a few times going under low bridges and overpasses, I've never seen one that wasn't clearly marked when it was really too low to meet the Federal limit.
When we workcamped near Bryce Canyon several years ago, a number of folks called the campground to cancel when they realized that the road into Bryce Canyon NP had a couple of very short tunnels that were something around 15 feet. They swore they could not get their rigs through those tunnels. Of course, there isn't an RV around that won't go through a 15 foot tunnel.
The best one was the 1 plus mile tunnel coming out the east entrance to Zion NP. That is the one where the rangers close the road to two way traffic, charge you ten bucks and RVs have to drive right down the middle of the road to have enough clearance. That one is a lot of fun. We have driven through it twice.
My personal nemisis is a railroad bridger south of Chatsworth, GA on US 411. Its not much higher than our rig and everytime I go through it, I am tempted to let the air out of the suspension system to make sure I clear. Of course, I always clear, but thoughts go through my mind everytime, things like, has the road department paved this road and decreased the clearance since the last time I drove through here!
I don't believe any of my Garmins or Street Atlas tell me bridge heights. At least I cannot find anything about them.