I did the guitar-on-a-plane thing once. I was flying from Buffalo to Albuquerque with a layover in Dallas, to visit a friend for a week. I wasn't going to attempt to bring anything valuable, but my old Yamaha classical guitar is a great player and sounds decent. I padded the inside of the chipboard case as well as I could and threw an extra strap around the outside, just in case they were going to make me check it. Luckily they were nice enough to let me bring it into the cabin on all 4 flights and one of the stewardesses was actually nice enough to stash it in the crew closet for me. Of course, a Starfire bass in a hardshell case takes up quite a bit more real estate, so I'm not sure they would have been as understanding if it was any bigger. It's always going to be a risk, at the discretion of the crew, unless you call the airline ahead of time and arrange to buy an extra seat ticket for your instrument. If you're flying with a bargain airline, that route might be worth it just for the peace of mind, but otherwise would likely be too expensive.
*I started writing this a couple of hours ago, but got interrupted by breakfast... apologies for the redundant seat ticket suggestion; Mav beat me to it!