Olympic champion Monica Puig also sailed through to the second round on a day in which none of the seeded players appeared.
Former world number five Bouchard has earmarked 2019 as her comeback year after sliding down rankings following a standout 2014 when she made the Wimbledon final and was a semi-finalist in Melbourne and Paris.
Now ranked 87th, the Canadian proved too strong for the 88th ranked Madison Brengle, taking just over an hour to beat the American 6-3, 6-3.
The 24-year-old mixed glimpses of her previous best with some unforced errors but overall gave herself a pass mark.
“I think it was OK,” Bouchard said.
“It was the first match of the year, so you never know what to expect from your level, so I’m happy I managed to handle my nerves.
“I liked that when things didn’t go so well I managed to turn it around relatively quickly, maybe a game or two went by, but then that was it and I managed to get back to playing my game.”
Puig was untroubled in her 6-3, 6-2 win over American wildcard Bethanie Mattek-Sands while 2017 champion Lauren Davis advanced with a 6-2, 6-2 win over Spain’s Lara Arruabarrena.
Davis will face the winner of the blockbuster clash on day two between former world number ones Venus Williams and Victoria Azarenka
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