I fly with my instrument at least one weekend a month. Most weekends involve multiple cities, so usually 3 legs, sometimes more. I have tried several airlines and read all the policies, and, despite what I have read, or FAA regulations, I have never been able to take my bass in the cabin, overhead, or closets. Maybe if I paid for priority boarding or first class, Id have a chance; I cant afford that so.... I have resolved to checking my bass and everything has been fine (knock on wood). I use the Pro Rectangular Electric Bass Case from SKB (1SKB-44PRO, which may only be available from SKB). I loosen my strings and snuggly pack the bass in with socks, underwear, t-shirts, for the trip. I roll up a pair of undies and them under the head stock at the nut for a little extra cushion should it go down hard, and then another folded pair at the top of the headstock. I usually drape a t-shirts over it before closing up the case. My guitarists do the same thing for their guitars and we've all had our instruments arrive safely every time. There is obviously some risk, but just part of the deal.
Had to gate check it, and luckily all turned out fine. 4 flights and not a scratch on the case. Seemed like it was at least handled with care. Good luck!