Cibulkova got past Yanina Wickmayer of Belgium 7-5, 6-2 in second-round play on the clay courts in Acapulco on a day when all but one seeded player advanced.
Cibulkova saved 3-of-6 breaks and Wickmayer saved 6-of-12.
Bouchard ousted Lara Arrubarrena of Spain 7-5, 6-2 and third-seeded Kaja Kanepi of Estonia eliminated Germany's Julia Goerges 6-7 (4-7), 6-4, 7-6 (8-6). Eighth-seeded Zhang Shuai of China bear Aleksandra Wozniak of Canada 6-1, 6-4.
Marina Erakovic of New Zealand defeated sixth-seeded Bojana Jovanovski of Serbia 6-1, 6-4.