Robson, who ensured she will move above Heather Watson in the national rankings by winning her first-round match, was the 16th seed at the claycourt event in Charleston, but again struggled with her serve against her fellow 19-year-old.
Canadian qualifier Bouchard triumphed 6-4 3-6 6-1 in a match lasting two hours six minutes, during which the Briton committed eight double-faults to her opponent’s three.
Robson began the week 42nd in the world rankings, which will be updated by the WTA on Monday, two places behind Watson, who has been diagnosed with glandular fever.
Watson is confident her absence from the WTA Tour will not be a lengthy one.
The 20-year-old reached the third round of the Australian Open in January, but has struggled for form this season.
After her first-round defeat by Ayumi Morita in Miami two weeks ago in a match she had led comfortably, Watson declared she was burnt out and needed a break from tennis.
She quickly retracted the statement and said she had simply been disappointed at losing the match and would carry on as planned with her schedule.
However, she headed home to Guernsey and pulled out of this week’s tournament in Charleston, and blood tests have confirmed Watson has glandular fever.
She said: “There is no prescription for this other than complete rest, but the good news is that the doctors have told me I am at the tail-end of the fever.”