I've been traveling with my bass now for about a year or so. Every week I'm flying with my bass. Here's what I've learned and this came from a Delta pilot......
There is no FAA regulation prohibiting musical instruments from being carried on an aircraft. Every now and then you run into someone who thinks they are doing the airline a great sservice by thinking they can enforce this. Now remember FAA regulations do not mean that the airline can't prohibit them.
I've been flying Delta and have had only one run in so far and this was at the gate, not the check in counter.
When this happens I usually ask for permission to see if the lead flight attendant or pilot has a problem with it. If you can get this far, there usually is no problem.
Lately I've only been able to get small 50-75 seaters out of Manchester NH. There literally is not enough space in the overhead. I have a hard time even getting my laptop up there.
This requires me to gate check my bass. When I get to my destination, they hand me my bass as I walk off the plane. This isn't so bad. Even if you do find space in the overhead, you run the risk of someone trying to jam their carry on into your bass.
Lately I've been using an SKB Bass Safe. This allow you to put your bass in a gig bag and then put that into an ATA approved case. Here's a link to the page on my site.
http://www.monotunesmusic.com/SKBBassSafe.htm.
Even then you still run the risk of the airline losing your luggage. There really is no absolute solution.