Bouchard, ranked eighth, is the only Canadian woman inside the WTA Tour's top 90, and the weight of expectation showed on home soil in Montreal - as the Wimbledon runner-up lost 6-0 2-6 6-0 to Rogers.
Bouchard held serve only twice in 10 attempts, as she was dealt a pair of bagels in a humiliating defeat at the WTA Premier hard-court event.
The 20-year-old, who has shot up the rankings after reaching the semis of every major so far in 2014, conceded the pressure got to her in the second-round affair.
"I was feeling the pressure on the court and I was feeling kind of match rusty," said Bouchard, who received a bye past the first round.
"I knew it would be kind of a difficult situation, but I'm happy I was able to turn things around and not let it get away completely."
Other second-round contests saw third seed Agnieszka Radwanska and eighth seed Victoria Azarenka progress.
Poland's Radwanska was too good for Czech Barbora Zahlavova Strycova 6-4 6-4, while Belarus' Azarenka grinded her way past France's Alize Cornet 6-4 2-6 6-4.
In first-round affairs, seeds Ana Ivanovic (nine), Caroline Wozniacki (11) and Carla Suarez Navarro (14) all progressed without much bother.
Serbia's Ivanovic cruised past Swiss Timea Bacsinszky 6-1 6-2, Dane Wozniacki thrashed Slovakian veteran Daniela Hantuchova 6-1 6-1 and Spaniard Suarez Navarro dismissed Serbian Bojana Jovanovski 6-4 6-3.
Major winners Venus Williams and Sam Stosur also moved into the second round.
American Williams saw off Russia's Anastasia Pavlyuchenkova 6-1 3-6 6-2, while Stosur eased past qualifier Monica Puig of Puerto Rico 6-2 6-2.
Another grand slam champion, Svetlana Kuznetsova, retired midway through her clash against Madison Keys with the young American leading 6-1 3-2.
There were good results for lucky losers Karolina Pliskova and Elena Vesnina, after the pair earned late entries into the main draw courtesy of withdrawals from Kurumi Nara (hip) and Andrea Petkovic (viral illness) respectively.
Czech Republic's Pliskova beat Belgian qualifier Yanina Wickmayer 6-2 6-1, while Russia's Vesnina - who also assumed the 16th seeding - edged Italy's Camila Giorgi 6-4 1-6 7-6 (7-1).
American qualifier Coco Vandeweghe continued her purple patch, downing China's Zhang Shuai 6-2 6-4.
Russia's Ekaterina Makarova obliterated Swiss Romina Oprandi 6-4 6-0, losing just four points in the second set.
Australian Casey Dellacqua was too good for Belgium's Kirsten Flipkens 6-0 4-6 6-2, France's Caroline Garcia downed Italian qualifier Karin Knapp 6-2 6-7 (5-7) 6-1 and Spain's Garbine Muguruza held off Canadian qualifier Stephanie Dubois 6-1 6-7 (4-7) 6-2.