You can easily raise your own mosquito larvae, just leave a bucket of water out covered enough to stop leaves and other stuff falling in it, and voila - mozzie wrigglers. Unless you have neighbours who spray chemical garden stuffs (sprays drift) it ought to be okay.
My fish loves brine shrimp, which you can buy live or as a 'kit' (sea monkeys!) to raise your own. He loves chasing them around, though the shrimp never manage to get very far... I froze half and defrost one now and then for a snack. In my house, we don't eat the pink ice cubes.
Other live food that I see a lot of folks recommend is blood worms or blackworms.
I'm a bit cautious about feeding my fish just any old bugs, even though wild bettas must eat a pile of whatever's hanging around near the water. The fly he ate wasn't my choice of snack for him! he did enjoy it though.