Bouchard, of Westmount, Que., lost 6-4, 6-4 to Dulgheru in the second singles match of the day.
Bouchard never looked confident in the match, committing 21 unforced errors. Dulgheru, ranked No. 72 in the world, broke Bouchard in the only break point opportunity of the second set at 3-3.
"I tried my best and I feel that I played a bit better than, say, 10 days ago," said Bouchard. "This is a step in the right direction."
Earlier in the day, Montreal's Francoise Abanda defeated Romania's Irina-Camelia Begu 4-6, 7-5, 6-4 in the opening singles match of the best-of-five tie.
The 18-year-old Montreal native needed two hours 39 minutes to register the victory.
"This was definitely the biggest win of my career, but I know I can play much better than today. I competed very well, but I played best last year at the Rogers Cup. I am just happy to win my first Fed Cup match here in my hometown," said Abanda.
On Sunday, Bouchard will play Begu while Abanda faces Dulgheru in singles before Ottawa's Gabriela Dabrowski and Toronto's Sharon Fichman take on Andreea Mitu and Raluca Olaru in doubles.
Canada is looking to maintain its position in the elite eight-team World Group for 2016.
Abanda started the match impressively, fighting off two break points in the first game before breaking Begu for a 2-0 lead. But the Romanian went on to register two breaks of her own en route to a 6-4 victory.
The Canadian forced a third and deciding set by winning the second 7-5.
Begu opened the third with a break, then held serve for a 2-0 advantage. But Abanda countered with two breaks of her own en route to a 5-3 advantage before clinching the 6-4 decision with a final break of her Romanian opponent.