Ash Ketchum dreamed of owning a Bulbasaur as his first Pokémon, but he broke his alarm clock and woke up late. When he arrived at Professor Oak's Laborotory, he realized it was too late and a trainer who wasn't late had already taken it.
Ash captured his own Bulbasaur in Bulbasaur and the Hidden Village, where it was guarding the abandoned Pokémon in the Hidden Village. After destroying Team Rocket's , Bulbasaur decided to join Ash and became one of his most reliable Pokémon. Halfway through his Johto journey, Ash sent Bulbasaur to Professor Oak's Laborotory to be an ambassador for the fighting Water and Grass Pokémon.
A Bulbasaur that used to belong to the Mayor of Trovitopolis appeared in The Mystery Menace. In his childhood, the mayor abandoned his Bulbasaur and sent it into the sewers when it wouldn't evolve into Ivysaur. Aided by Misty and Tracey, Ash found the abandoned Bulbasaur while searching for his own, which had gone missing. After defeating the arrogant mayor and his personal SWAT team, Ash and company left the Bulbasaur, which had grown rather large in its time in the sewers, with Nurse Joy.
May captured a Bulbasaur in Grass Hysteria, when she was seperated from the group. Before the Kanto Battle Frontier saga, she left Bulbasaur with Ash's Bulbasaur at Professor Oak's Laborotory. She retrieved it during her travels in Johto, where it evolved all the way into a Venusaur.
In Journey to the Starting Line, Gilbert, the son of the mayor of Pallet Town, was supposed to start his journey as a Pokémon Trainer with one of the three Kanto starter Pokémon, but they were scared off by Ash's Tauros. Professor Oak, Tracey, Delia, and Gilbert set out to find them. The Bulbasaur was the last one to be found and it was stuck in a tree that was surrounded by a group of Primeape. In the end, Bulbasaur was the one that Gilbert decided to start with.
Multiple Bulbasaur appeared in Battle Aboard the St. Anne. A Bulbasaur also appeared in Pokémon Fashion Flash and The Breeding Center Secret. A Bulbasaur under the ownership of an unknown Trainer, appeared in Friends to the End, during the closing ceremonies of the Indigo League. A Bulbasaur was used by one of the students of the Pokémon Trainer's School in Gonna Rule the School!. A Bulbasaur appeared in the opening of Jirachi: Wish Maker. A Bulbasaur was one of the starter Pokémon at Professor Oak's Laboratory in The Right Place and the Right Mime. A Bulbasaur made a brief appearance under the ownership of a Trainer in the Lily of the Valley Conference in An Old Family Blend!.