Great advice!
I fly with my guitar ALOT.
Firstly, I can't recommend Hiscox cases enough. They're absolutely killer cases and Pete and the guys are really nice people and can't help you enough.
Here are a few things I'd recommend.
1. Ask to gate check the guitar when you're checking in - basically take your guitar through security then have it checked in at the gate which means it will be first on and last off for sure, and you've witnessed all of it's security checks.
2. Before gate checking the guitar simply ask if you can take it on the plane. This is at their discretion so just ask someone who looks nice and be real nice to them. I've NEVER had someone say no. If the planes full they have always walked me through to first class where I've put it in one of their wardrobes/cloakrooms. This is with various airlines.
3. Oversized luggage at Heathrow are complete and utter arrogant idiots. Would recommend taking it to them as a last resort and gate check is a better option.
4. Fragile stickers don't make a difference other than peace of mind. Get a good case made for the shape of your bass.
Hope this helps anyone flying! Buying a seat is also a great option but I'm way too tight for that! :-)