Fields has been sidelined since exiting an Oct. 15 loss to the Vikings in the third quarter with a dislocated right thumb he sustained when he landed awkwardly while being sacked.
Bagent made his first NFL start last weekend at Soldier Field, completing 21 of 29 passes for 162 yards with one touchdown, no turnovers and a 97.2 passer rating in a 30-12 win over the Raiders. In Sunday night's 30-13 loss to the Chargers in Los Angeles, he connected on 25 of 37 passes for 232 yards with two interceptions and a 62.0 passer rating.
"The first game he was good and what was different was the takeaways," Eberflus said. "We've got to do a good job of protecting the ball, being on the positive side or the even side of that turnover battle and that was really the difference.
"I still think he delivered the ball well. He took some shots down the field you didn't see in the first game, which was exciting to see. We're going to continue to stretch the field vertically and horizontally."
Eberflus said Monday that Fields is improving but remains week-to-week.
"Justin continues to work with the trainers," Eberflus said. "Until he gets back healthy, Tyson will be our quarterback for now."
In other injury news, Eberflus revealed that safety Jaquan Brisker is in concussion protocol. The Bears coach shared the timeline with reporters that culminated in the second-year pro sitting out Sunday night's game.
"Sunday, Monday, he checked out fine with the evaluation and with an independent neurologist, being cleared from the concussion," Eberflus said. "He was all set. Then Tuesday he reported that he was ill and had a fever. That persisted through Tuesday, Wednesday, Thursday. And Friday we brought him into the building. He was in here then, still not feeling well. We ruled him out Saturday and then he wasn't feeling well. His illness cleared Saturday, and then Sunday he still felt a little bit off in terms of having different symptoms and those types of things. We got him re-evaluated [Monday] and now he's back into concussion protocol.
"We were working with Jaquan the whole way, talking to him, making sure he was squared away," Eberflus said. "The most important thing is our players' safety and health. Jaquan did a very good job communicating with us, and the training staff did a really good job, too, of seeing this thing all the way through."
Eberflus also said that the knee injury middle linebacker Tremaine Edmunds sustained early in the second half Sunday night will be further evaluated over the next couple days, but it appears that he avoided a serious issue.
"It seemed that way," Eberflus said. "He came back and played a few plays, and that's always a good sign. We'll see."