It depends on the number of fish, species and their oxygen requirements, Ben. I did have some fish in the bags for 36-48 hours but that was because I was using our van and ship to travel thousands of miles instead of flights.
this all depends like everyone else said. youve got to think, a bunch of companies ship fish, next day delivry, and have no problems, so thats at least 24 hrs. i have had a fish in a bag for like 5 HRS, dont ask.
If the fish starts to look 'suffocatey', open the bag and stir the surface of the water with a finger (or something cleaner) to oxygenate the water. Then re-inflate with lung air (it's still loaded with oxygen, trust me) and close 'er up for safe travels. I've done it. It helped a lot.