The third-seeded Bouchard, from Westmount, Que., was coming off a semifinal appearance at the French Open. She took the opening set before the unseeded American came back for the 2-6, 6-3, 6-3 victory.
Top-seeded Simona Halep, the French Open runner-up, beat Olga Govortsova of Belarus 7-5, 6-2. Halep broke for a 6-5 lead in the first set and then again in the first game of the second set.
She will face Annika Beck of Germany in the second round.
Also Tuesday, Yaroslava Shvedova upset second-seeded Dominika Cibulkova 6-2, 3-6, 6-3.
In the men's draw, second-seeded Fernando Verdasco of Spain overcame a shaky performance to beat Paul-Henri Mathieu of France 2-6, 6-4, 6-4.
Verdasco, the highest seed on the men's side after countryman David Ferrer pulled out of the grass-court warmup for Wimbledon, served 13 aces but also had 15 double-faults.
After a poor first set he broke Mathieu early in the second. In the third, Verdasco saved two break points in his first service game and then broke Mathieu in the fifth game with a crosscourt backhand return.
Third-seeded Roberto Bautista Agut beat Daniel Gimeno-Traver 6-1, 6-3 and Nicolas Mahut overcame Kimmer Coppejans 6-3, 3-6, 6-3.