Instructions
Challenge and beat Falkner, Bugsy, Whitney and Morty to get the first four Johto badges for your Trainer Card. Navigate through Route 41 to reach Cianwood City. Go to the Safari Zone on the west side of this city.
Talk to the Safari Zone Warden. Catch and give him a Geodude and a Sandshrew to complete his quest. You will be able to decorate the Safari Zone with blocks upon completing the quest. Once you place a certain combination of blocks in the Safari Zone, a new Pokemon will appear there after one to two months.
Defeat the Elite Four and go to Professor Elm. Go to the port in Olivine City and speak to Professor Oak to get the National Pokedex. Obtain nine Trees, Stumps or Branches (Forest Objects) and 19 Small Rocks, Big Rocks or Mossy Rocks (Peak Objects) from the Safari Zone Warden.
Place the Forest and Peak Objects in the Swamp section of the Safari Zone. Leave the objects in the Swamp for at least 110 days. Level-45 Bagon will start to appear in the Swamp on the 111th day.
Look for Bagon in the long grass of the Swamp section. Run away from Pokemon other than Bagon. Cast "Mud" at the Pokemon to make it easier to catch. Fling "Bait" at the Bagon to prevent it from running away. Throw Safari Balls at the Bagon until you catch it.