Here is how I ship bettas:
Do 100% water change on betta's tank 72 hours before shipping date. Fast the fish for 48-24 hours before shipping. Then I use a turkey baster to take some tank water and squirt into shipping bag. Not too much. You will need enough water to cover the betta no matter which way the bag is turned. Then the betta goes in the bag. I use an air pump with airline hose to squirt in some extra air and twist the bag and tie it. Then I cut off the extra length of bag, turn it over and slip it into another bag. Tie that one closed, cut off the extra and sit the bag in a foam-lined box. Packing peanuts are used as filler to make sure the bag stays firmly in place and provides extra insulation. If a heat pack is needed then it is activated, wrapped in one layer of newspaper and taped to bottom of foam lid. The foam lid goes on and then I seal up the box. Simple as that