There was way to much water and not enough air in that bag. Bettas are air breather's the dont breath air from the water like other fish do. If you went under water and only had a 5 gallon bucket full of air and keep breathing your going to run out of air. When shipping a betta it's not like shipping other fish. You only fill the bag up with enough water, Where it just cover's the bettas dorsal fin. Not so much water that he can really swim around. You want way more air then there is water in the bag. And every breeder i have ordered from has done this. Respectable breeder's and great thai breeders all ship this way. what if the fish was in the mail a little longer than it was supposed to or something happen it got stuck in the mail. You want all that air trust me. It seem's mean thats why i called and asked when i got my bettas. They only need a little water to keep them wet thats it but they need a lot of air.
Other fish slowly breath oxygen from the water so it do use as much. But with the betta breathing air the use a lot out of the bag thats why you want to put so much in it....
I agree with FB, bettas need more air than water (so to speak). Long finned bettas need more water than short finned. water level should cover all fins nicely. Bag width should be a bit longer than the fish's length (at least).
Would like to add, bag should be in up right position (not laying on side) so when moved, the water doesn't shake too much. When shipping 2 or more, it is best to cover the plastic bag with paper so that the fish can't see each other (to avoid stress and fighting).
To trap as much air in bag; place it on something (after filled with betta) and make sure the bag is fully up right. Then pinch (?) and fold the top (about 1 cm) at a time until the bag is rather tight (?). Twist it to make it tight and fasten it with rubber band. This way (if done correctly) less air is likely to escape.