If you get a Mareep, found at route 32, and train it up to like 15, you can take out Falkner *snaps* just like that. Now for Bugzy, if you started with Cyndaquil, you shouldn't have any problems with him. The best place to train Cyndaquil that early in the game is Sprout Tower, in Violet City. If you started with Totadile, or Chikorita, sorry, can't help you there.
May make random appearances every-so-often. Trying to officially return...
POKEMON BLACK FRIEND CODE: 1249-2602-6566
POKEMON BLACK2 FRIEND CODE: 1679-1583-9820
POKEMON Y FRIEND CODE: 3308-5051-2299