Johto
Bayleef was introduced in The Chikorita Rescue as a Chikorita. Chikorita was especially stubborn, going so far as to fight against Ash's Charizard despite obvious overwhelming odds; she was injured in the process. Team Rocket tried to convince the stubborn Pokémon to join them, but Ash eventually won her confidence.
Chikorita later was used in Once In a Blue Moon to try getting the GS Ball back. However, Chikorita only wanted to be affectionate, so when Ash told Chikorita not to, Chikorita got angry and hit Ash with its leaf.
Chikorita developed what seemed to be a crush on Ash, constantly fighting for his attention and trying to get his approval. In Gym Battles, she lost to Falkner's Hoothoot and defeated Bugsy's Spinarak.
In Current Events, Chikorita evolved into Bayleef to protect Ash from Team Rocket. However, it took a while for the amorous Pokémon to realize that she had grown so much - she continued to act as though she was still small enough to leap into Ash's arms for quite some time.
In Ash's Gym Battle against Chuck, Bayleef defeated his Poliwrath and Machoke. At the Silver Conference she lost to Gary's Blastoise despite a type advantage, but made up for it the next day by defeating Harrison's Houndoom, against whom she had a type disadvantage. Bayleef showed itself to be a strong and powerful Pokémon on Ash's Johto team. Ash left Bayleef with Professor Oak when he left for Hoenn.
Bayleef's personality is stubborn, sometimes violent, and passionate. She easily gets jealous of the attention Ash's other Pokémon receive - especially Pikachu. Some of her more extreme personality traits seemed to have mellowed with evolution, however.
Sinnoh
It appeared in DP182 alongside Ash's other Pokémon. She was sent to Ash from Prof. Oak's lab and tackled Barry. Then, she found Ash and tackled him, too. When he tried to return her to her Poké Ball, she took it in her mouth, wanting to spend more time with Ash. She later helped destroy the hands of one of Team Rocket's mechas, and afterwards, was sent back to Professor Oak's lab.
Ash plans to use Bayleef later on in the Sinnoh League.