Season 3. Bernadette makes her first appearance in "The Creepy Candy Coating Corollary" where she meets Howard via Penny and goes out to dinner with her and Leonard who are dating.

What episode does Bernadette appear?

The third season saw the first appearances of future main cast members Melissa Rauch as Bernadette Rostenkowski in "The Creepy Candy Coating Corollary" and Mayim Bialik as Dr. Amy Farrah Fowler in the season finale "The Lunar Excitation".

Did Howard and Bernadette get divorced?

Season 4. "The Hot Troll Deviation"- It is revealed that Howard and Bernadette broke up because she caught Howard having cyber-sex on World of Warcraft with Glacinda the Troll. Howard convinces Penny to help him to get Bernadette to talk to him.