Bruce, 20, who was named the No. 1 prospect in 2008 by MiLB.com and Baseball America, was seeking to become the Reds' starting center fielder in a spring battle that started with Ryan Freel and Norris Hopper.
The race tightened once center fielder Corey Patterson was signed to a Minor League contract and invited to camp at the urging of Baker, who previously managed the veteran when they were with the Cubs. Like Bruce, Patterson is a left-handed hitter.
"When they signed Patterson, I knew the writing was on the wall," Bruce said. "They have an idea of what they wanted to do. I'll keep doing my thing and try to force the issue this season and see them soon."
Bruce didn't have a bad spring at the plate, but he probably needed to have a great camp to erase any doubts about his big league chances at this early stage of his career. He batted .262 (11-for-42) with three RBIs in 16 games.
"Jay is real close, especially for a man who hasn't had much Minor League experience," Baker said. "It won't take him too long. It's nothing that he did wrong. Just tighten up your game. Experience will do that. Desire and determination will do the rest."
After starting out hot, with hits in each of his first five games, Bruce's cause wasn't helped when he sustained a mild strain of his left quadriceps muscle on March 2. He missed nearly a week, and during that time, the Reds signed Patterson.
Once he returned from the injury, Bruce struggled to regain traction. Meanwhile, Patterson has played his way into a roster spot. Entering Thursday, he was batting .455 (10-for-22).
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The Reds preferred to give Bruce everyday at-bats in Triple-A rather than keep him idling on their big league bench. They also want him to stay for good when his big league promotion eventually comes.
"When he gets here, he'll be here a long time," Baker said. "I know what it's like to go back and forth. I went back and forth. It's a tough thing. You reach your goal and go backwards, reach it again and go backwards.
"It wasn't something we wanted to do but it's something we needed to do right now. There's now and there's the future. A lot of times, as a young person, a week seems like a month and a month seems like a year."
As for the center-field battle, Baker appears to have made up his mind but isn't sharing, yet.
"I have a plan," he said. "Everybody wants to know the plan. Everybody is guessing the plan. We'll just let the plan work itself out."
In the other cuts, Cincinnati optioned outfielder Drew T. Anderson and reliever Marcus McBeth to Louisville. Like Bruce, pitchers Josh Roenicke and Tom Shearn were reassigned to the Minor League camp.
The Reds have 44 players remaining in camp and need to be down to 25 when they break camp next week.