But it's unknown yet when it will continue.
"I felt like we needed a spark," Arizona coach Steve Wilks said. "We got off to an early start -- 14 points -- got a little stagnant there and wanted to try to spark the team. That's the reason why I made the decision."
After Wilks whispered something in Bradford's ear following his lost fumble with 11:33 left in the game, quarterbacks coach Byron Leftwich walked over to Rosen and said, "Get ready," Rosen recalled. A few minutes later, Rosen took the field.
Bradford left the game with 157 yards on 13-for-19 passing and two touchdowns. He had also thrown two interceptions and lost a fumble.
"It's Coach's decision," Bradford said. "I respect his decision. More than anything, just disappointed that I put the team in such a bad spot today."
Rosen completed 3 of 6 passes for 27 yards on his opening drive, but he threw an interception on fourth-and-5 with 1:10 remaining. The Cardinals got the ball back one final time, with Rosen completing a 9-yard pass to Christian Kirk and rushing for 12 yards before taking a sack as time ran out.
"I thought he looked pretty good, inconsistent in the end," Wilks said. "We've got to do a good job, forced protection, giving him time. But under the circumstances right there, being thrown into the game at that time, I thought he did well."
Rosen said his goal was to march the Cardinals down the field for a game-winning field goal. Even though that didn't happen Sunday, Rosen said, "Hopefully, I'll find my groove."
Wilks wouldn't commit to a quarterback for next week's game against the Seattle Seahawks after Sunday's loss, saying he wants to evaluate both quarterbacks before making a decision.
"It's a lot that goes into it, and it's too early to go into right now," Wilks said. "You have to look at every situation. How are we playing up front? How are we doing? All of that, just from a standpoint of execution and trying to get the guys in the right position to be successful across the board.
"I'm going to look at everything to make sure I make the right decision for this team."
Rosen wasn't disappointed in his play in his brief appearance Sunday but felt that he could have performed better.
"I don't know, sort of," Rosen said. "I guess you could say I'm kind of content that I got to get out there and sort of understand and get the feel of a real NFL game, but I definitely could play a lot better.
"So I'm looking forward to getting better in the weeks to come."
The Cardinals' offensive struggles continued Sunday afternoon against the Bears, even after the playbook was scaled down to a more manageable and understandable size.
The offense rolled to two quick touchdowns in the first quarter. After that, it slowly ground to a halt. The Cardinals didn't gain a yard in the second quarter and gained just 30 in the third quarter while not scoring another point.
What ended Bradford's day was the fumble he lost after trying to scramble on a broken play early in the fourth. Bradford thought he put the Cardinals "in a bad spot" in the second half.
"Kind of the same thing, it seemed like," Bradford said. "We didn't convert a third down. Next thing you know, you look up, and it is halftime and we have run 15 plays again. I'm not exactly sure what happened after that start, but obviously, it couldn't have gone much better the first drive."
Sunday's performance was a continuation of the offense's poor play of the first two weeks, when it scored just six points. Heading into the contest, Arizona ranked last in the NFL in yards per game, passing yards per game and per play, first downs per game, third-down percentage, average time of possession, and points per game.
Publicly, the Cardinals exuded confidence that the offensive woes could be corrected this week. But that was not case Sunday, and Arizona turned to Rosen, its quarterback of the future, with the hope that he would provide a spark.
Rosen was drafted 10th overall out of UCLA in April, after the Cardinals traded up five spots to get him. He has been patiently waiting under Bradford's wings for his opportunity.
On Thursday, Cards offensive coordinator Mike McCoy didn't answer a direct question about how ready Rosen -- specifically -- was to play, if needed, saying, "I think everybody's ready to play."
Rosen, who beat Mike Glennon to win the backup job during training camp, said he was ready to play every week.
"Anything can happen," Rosen said. "Everyone should prepare as if they are the guy, they are the starter."