Is this transportation method OK for my bettas?

Honestly, your bettas will be fine for two weeks without food. Bettas are hardy fish that accept daily food, but can go long periods without food. I'm talking more than a month without problems. It's probably better for your fish than trying to transport them a long distance even in a large container. Transportation is very stressful for fish, and even transferring between one tank to another is quite stressful.