The left-hander gave up two runs in two innings in an 8-5 loss against the Toronto Blue Jays.
Bedard hit the first batter he faced, gave up a double to Travis Snider, walked two and struck out one.
"Just trying to get my work in, trying to throw strikes," Bedard said. "I threw everything, like I would in the regular season. It'll take time. First game."
Snider was 2 for 4 with 3 RBIs for the Jays. He had a run-scoring single in the fourth. In the sixth, Snider got two RBIs with a grounder to reliever Evan Meek.
First baseman Jeff Clement didn't cover the bag, so Meek had to outrun Snider for the out. Jonathan Diaz scored from third base and Anthony Gose scored from second on the play.
"We were sloppy," Pirates manager Clint Hurdle said. "Our awareness wasn't where it needs to be to play a game -- a major league game, a minor league game or an exhibition. It's a lack of focus."
Bedard signed a one-year, $4.5 million contract in December. With A.J. Burnett (fractured orbital bone) out until at least early May, Bedard could be the Pirates' opening day starter.
"We're more curious about where (Bedard) is in his first outing in the regular season than today," general manager Neal Huntington said. "I've seen too many veteran pitchers get knocked around in their spring training debut or their last start of spring training, and then they find another gear when the season opens."
The two best seasons of Bedard's career were 2006 and `07 with the Baltimore Orioles. He won a total of 28 games with a 3.47 ERA and averaged 9.3 strikeouts per nine innings. He finished fifth in the Cy Young voting in 2007.
Bedard has had three operations over the past 10 years, including shoulder surgery in 2010. Last season, he was out for two weeks in September due to a sore knee.
His struggles in the second half last season -- Bedard won just one of his final eight starts with the Boston Red Sox -- caused some teams to back away this offseason.
"If he stays healthy, we believe he's going to pitch well," Huntington said. "He's not that far removed from being one of the best starters in the American League."
"I felt free and easy, nice and loose," Laffey said. "For the most part, I kept the ball down and was able to change speeds. I was pleased with it."
Laffey signed with Toronto figuring he has a good shot to win a spot in the starting rotation. But he would be willing to take a bullpen job if it keeps him from going to Triple-A Las Vegas.
"It's all about being here in the big leagues," Laffey said. "I feel like I'm a big league pitcher with big league stuff. I think I've proven I can be consistent at this level."
Play was halted briefly in the bottom of the sixth inning when a gray cat scampered across the field behind home plate. The cat jumped into the stands and disappeared under the left field bleachers. ... Blue Jays reliever Jesse Litsch will be shut down for six weeks after having an arthroscopic procedure to clean an infection out of his right shoulder. Litsch, who's expected to be a middle/long reliever this year, was released from the hospital Saturday. "I talked to him and he is very upbeat," manager John Farrell said. Litsch spent time on the disabled list last season due to an impingement in his shoulder. ... Right-hander Henderson Alvarez had been scheduled to start Sunday for the Blue Jays, but he was pushed back to Monday for extra rest. ... Barajas went 2 for 2 with two RBIs. Nick Evans hit a solo homer for the Pirates. ... Pirates infielder Josh Harrison was scratched as a precaution after being hit on the elbow by a pitch on Saturday. X-rays were negative. ... Pirates right-hander Charlie Morton, who had hip surgery in October, will pitch Wednesday in an intrasquad game. ... The Pirates will play the Baltimore Orioles at 7 p.m. Monday.