After exiting the tunnel you'll find Team Rocket guarding a well and the local Gym. Well it seems that Team Rocket has kidnapped all the Slowpokes from the town.

First you'll need to talk to Kurt in the house right above the Gym. He'll move the Rocket member guarding the well. Next it's your turn to defeat the Rocket members.  Once defeated, the Gym will open and you'll be able to fight Bugsy.

Later after you get HM 04, Strength, return to Slowpoke Well and go to the Lower Level. Here you'll find the King's Rock (which will evolve Slowpoke or Poliwhirl when you attach it to them and trade them to another Game Boy.) You can also find TM 18, Rain Dance.

After defeating the Rocket members in the well, Kurt will take you back to his house and give you a Lure Ball. Lure Balls are used to catch Pokemon hooked by a Rod (from fishing). He'll also make more special Pokeballs from Apricorns that you can get from plants scattered throughout the Johto region.

For example, the plant behind his house will give you White Apricorns, and they are then made into a Fast Ball. Fast Balls are used to catch fast Pokemon.

Bugsy uses 3 Bug Pokemon. So if you chose Cyndaquil as your starter Pokemon you will really have the advantage, especially against Scyther.

Bugsy will give you the Hive Badge which lets all Pokemon up to level 30 obey you and lets your Pokemon use Cut outside of battle. He also gives you TM49, Fury Cutter.