Mousehole, you don't need reflexes. Trust me...I have NONE. All you do is hit Y to go into your inventory and then equip your net. All action is stopped at that point so the bees don't come. What I do is hit the shoulder button to run really fast a few paces away, open my inventory, equip my net, then close inventory to restore action, and as soon as the bees come close, but not TOO close, hit A. I usually catch them pretty easily now and the 2,000 or 2,500 they are worth at Re-Tail is GREAT! Also, sometimes I keep one or two and the villagers want to trade for them or buy them.
It's not that bad, really. Once I read that you can stop the action it isn't too hard to catch one. Just try once or twice to get the timing of how close the swarm comes to you and you'll catch on. I promise.