The Canadian's loss saw her slip to a 0-2 record in the Red Group and she now needs an emphatic victory over Serena Williams in her last round-robin match to stand any chance of making the semi-finals in Singapore.
Bouchard, who has struggled with injury in recent weeks, is playing the tournament for the first time in her career after a 2014 that saw her reach the semi-finals at the Australian and French Open, before contesting the Wimbledon final.
After a lacklustre showing in the 6-1 6-3 loss to Ivanovic it was suggested that the world number five was perhaps struggling with the grandeur of the tournament, a notion she rejected.
"I've been asked a few times about it being my first time here," she told reporters. "That [being overwhelmed] never crossed my mind.
"I've done a lot of first things this year. You have to do everything first at some point in your life. I just was excited to come here. I see it as the fifth grand slam.
"I wish I could have had better results so far, but it's a great experience. It's about learning. Hopefully I can be back many more times."
Ivanovic, who had lost each of her previous two encounters with Bouchard, stated that a quick start and aggressive tennis was the key to her victory.
"I definitely started very well. I was very happy with that. I knew I was having a tough match against her," she commented.
"I lost to her twice before. I really tried to be aggressive. From the beginning I was playing well.
"That first game was important to hold my serve, and then after that I managed to break her straight away. That gave me confidence."
Ivanovic now has a 1-1 record and faces Simona Halep in her final group match.