German world number nine Kerber eased past New Zealand's Marina Erakovic 6-4 6-2 while Canadian Bouchard dropped just one game in her victory over Anastasia Rodionova.
Number one seed Kerber will fancy her chances of reaching a third final of the year and she made light work of Erakovic to book a second-round clash with compatriot Anna-Lena Friedsam.
Despite double-faulting five times during the match, Kerber was always in control as she picked up her first win of the clay-court season.
"I've never played against (Erakovic)," Kerber told the WTA website.
"I think it will be interesting to play against another German here in Germany. I'm looking forward to it and hope that I can have some more matches before (the French Open in) Paris."
Bouchard was another success story on Tuesday as the world number 19 won the first nine games to move within two wins of the final.
However, sixth seed Kurumi Nara saw her campaign ended by world number 72 Yaroslava Shvedova
Nara came unstuck against Kazakhstan's Shvedova - going down 6-4 6-2 after dropping serve six times during the match.
Karolina Pliskova remains on course for a quarter-final clash with Kerber after the Czech world number 64 saw off Alison Van Uytvanck.
The Belgian put up stubborn resistance early on in the first-round clash but eventually came up short - losing 7-6 (7-5) 6-3 - with Italian Karin Knapp also moving into the quarter-finals.
Knapp was forced to fight back from 3-1 down in the first but enjoyed an easier second set in her 6-3 6-3 win over Polona Hercog.