When in doubt, "don't ask and don't tell."

A looong time ago, I was given a couple of shotguns by my Grandfater.  I rode the Greydog out of Idaho with the guns, uncased,  in the overhead.  No buddy batted an eye.  It was a different and better time!

Assuming both ends of her trip are in a valid CCW area she should have no trouble- remember- CONCEALED!  No way I'd let my better half go on a bus trip without protection.....[8P]

I can only tell you what the policy was 4 years ago when I was foolish enough to be driving the Dogs.   Figure that it can't have changed for the better.  It was "No guns on the bus" exceptions were made for law enforcement on duty of course, and there isn't any way that I'd have told a cop who was riding with me "no you can't".  More than likely would have muttered about not being allowed to and welcomed that someone fairly reasonable on the bus was armed.

As for security it really depends on the terminal where you get on the bus, and where you travel though.  Anything from everyone getting wanded in A FEW of the major terminals, to absolutely nothing in the smaller (the majority) of stops.  Heck the company didn't provide or even officially permit cell phones until the last couple of years.

In any event getting caught with a gun on a bus is almost definitely going to get you thrown off at the least or a ride with the local cops.

Had a drug dog pull a bag (unmarked, untagged) from under the bus one morning in Cincinnati, and genius game running off yelling 'hey that’s my bag', couple kilos of cocaine and a loaded pistol from under the bus and another in the guys belt [rolleyes]  If he'd stayed quiet on it there wasn't anything to tie him to the bag or otherwise call attention to himself.

I do miss the driving but the safety issues and mismanagement were just to much to contend with

The real-world answer is "don't get caught".

Transporting firearms is not the same thing as carrying concealed.  Local, state, and federal law makes exceptions for transporting weapons.  If you have some reason to claim that you are transporting the weapon(and your not doing this commercially) and keep it out of sight, you will not have a problem.  And I doubt that any charges could actually "stick", if something ugly where to happen.