In a clash of the only two players making their first appearance at the season-ending championships, Halep lost only four points when getting her first serve into play.
"Maybe I can believe," Halep said. "I have the chance to win this tournament, but I don't want to think about this."
Bouchard, from Westmount, Que., was well below her best, racking up 30 unforced errors against 11 from Halep.
"Going for it is always my game style but today there was definitely a lack of consistency," Bouchard said. "I didn't feel match sharp, but I feel like I can build on this and I still have another match, which is a bit of a positive."
Bouchard will next face Ana Ivanovic on Wednesday while Halep will face Serena Williams. Williams won her opening match earlier on Monday, beating Ivanovic 6-4, 6-4 for her 16th consecutive victory at the finals.
The top-ranked Williams came into the season-ending tournament after injuries forced her out of her previous two tournaments and with the off-court distraction of disparaging comments about her from Russian tennis official Shamil Tarpischev.
Before the WTA Finals, Williams retired from the China Open and Wuhan Open because of illness and a left knee injury that had her in doubt for Singapore. But with the win over Ivanovic, she closed in on Martina Navratilova's record of 21 straight wins at the tournament.
"I just found out last time that I was 15 matches and I was like, 'Oh boy, not another streak,'" Williams said. "So now I'm 16 and, gosh, here we go again."
The top-ranked Williams was shaky in her opening service game, having to save two break points, but soon settled and took a 4-1 lead. Ivanovic got back on serve at 4-4 and had a crucial break opportunity to go up 5-4 but missed a volley.
"That was a huge point but it was actually quite a hard volley, the ball was dropping fast and I didn't come in fast enough," Ivanovic said. "I kind of got down a little bit on myself, then I rushed a little bit that (next) service game, so that was a little bit disappointing."
In the final game of the opening set, Ivanovic fell behind 0-40 and eventually dropped serve on a double-fault — one of seven she made during the match.
Ivanovic came from a set down to beat Williams at the Australian Open, and looked capable of a similar comeback when she broke in the opening game of the second set, but the American immediately broke back.
Williams served 12 aces and improved her record against Ivanovic to 8-1 despite her injury-interrupted preparation.
"I felt the knee a little bit, but compared to what it was in Beijing, it just feels so much better," Williams said. "I was up 4-1 in the first set and cruising and she does what she does best. I felt my energy level got a little low and then I just tried to do everything I can to bring my energy level up to just to fight."
In Tuesday's White Group matches, Maria Sharapova takes on Caroline Wozniacki and Petra Kvitova faces Agnieszka Radwanska.