Are you checking it or bringing it in the cabin? I have done both.
If it's going in the overhead bin, then the pressure change is only to the equivalent of 6,000 feet altitude (which is like Denver). Not such a big deal. In this case I'd be more concerned about other passengers smashing their luggage into it.
However, I'm not sure you can reliably expect them to let you put it in the overhead bin (and certainly only with a gig bag).
If you check it then you will need an ATA flight case. You might want to tune down a bit, but I don't think you need to completely release the tension on the strings. I never have. The temperature is more likely to affect the instrument than the pressure, IMO. It is about -40 at altitude. My flight case has three layers of foam, top and bottom are solid foam and the middle layer is the same thickness as the bass with a cutout to the shape of the instrument. The instrument is held securely with foam all around. Hopefully the foam provides some level of insulation so that the adjustment to the change in temperature occurs a little more slowly.
Good luck.
Jim