The Bears followed with their fourth TD on their first five drives, taking a 28-0 lead on running back Ian Wheeler's 1-yard run on fourth-and-goal with 1:50 left in the half.
Cairo Santos' 40-yard field goal made it 31-0 midway through the third quarter.
The Bills' best chance to score was thwarted by linebacker Amen Ogbongbemiga, who generated the game's only takeaway by stripping running back Frank Gore Jr. after an 11-yard catch. Defensive end Xavier Carlton recovered the fumble at the Bears' 14.
Bagent was replaced by Austin Reed late in the third period after completing 13 of 22 passes for 196 yards with 1 TD and a 103.6 passer rating.
Wheeler scored his second touchdown of the game on a 10-yard run, extending the Bears' lead to 38-0 with 9:35 remaining in the fourth quarter.