Steelers head coach Mike Tomlin told reporters postgame the team believed Bush suffered a "significant" knee injury, according to ESPN's Brooke Pryor.
Bush exited before halftime and was later declared out for the rest of the afternoon. Robert Spillane finished the contest with six tackles after replacing him.
"Spillane more than answered the bell," Tomlin said. He added that players who "make plays in special teams, that's usually a precursor to making plays on defense."
Bush, the Steelers' first-round pick in 2019, came into Week 6 with 21 tackles, three pass breakups, and half a sack over four games. The 22-year-old has anchored the linebacking corps in Pittsburgh since his NFL debut.
"We'll put together a formula in the interim," Tomlin responded when asked about a replacement plan for Bush. "Believe it."
As a rookie last season, Bush notched 109 tackles, four pass breakups, two interceptions, and one sack.
The Steelers moved to 5-0 with their latest triumph.