I've heard conflicting stories about whether it's needed or not, but for me it helps to go inside a building (the museum or Nook's Cranny), talk to the NPC there (pretend you're donating or selling something), then go out again.
You need to be outside before the clock jumps to 4 or 9, then go to the side of your island where your balloons are spawning (for Northern Hemisphere islands, this means to the west side beaches during the day and the east side in the evening). Then you wait, and when the time is there for balloons to spawn, run up and down the beach. Sometimes it can take a minute or a bit more for a balloon to reach the island (they spawn at the edge of your map, over the sea, and their speed depends on the amount of wind), so don't give up too soon! If you shot one or there seems to be none, repeat the process of going inside and talking.
This way, I can usually hunt down 8-10 balloons in an hour. I've tried doing this without going inside, but for me, it could take 20 minutes or more for the next balloon to spawn that way.