"There is more to being ready than just hits," Baker said on Sunday before Cincinnati's series finale in Atlanta.
Bruce missed two months after breaking his right wrist trying to make a catch in New York, and he's just getting back into complete playing shape after being out so long.
The outfielder will rejoin the Reds in Colorado during a four-game series that opens on Monday, but it probably won't be until after Louisville's regular season ends Monday.
"I wish there was more time," Baker said. "I wish there was another week."
Bruce was 0-for-6 with a walk in his first two rehab games, but he was 3-for-5 for Louisville in a 7-4 victory in Indianapolis on Saturday. Both hits were singles and he scored twice.
It had been a difficult season for Bruce before he was injured. The 22-year-old had 18 homers and 41 RBIs in 83 games, but he was batting just .207.
Ryan Hanigan began a rehab assignment with Bruce on Thursday, and the catcher also had three hits and scored twice on Saturday. He was 5-for-12 with a double in his first three games.
Hanigan, who suffered a concussion, is eligible to come off the disabled list on Wednesday. Bruce is eligible immediately.
Guy Curtright is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.