The 29-year-old right-hander was 9-10 with a 4.18 ERA in 31 outings last year, including 29 starts. In his final 18 games of the season, Bush went 7-3 with a 3.23 ERA. He was the starter and winning pitcher in the only game the Brewers won during their first-round playoff series against Philadelphia.
Bush made $2.5 million last season.
Four Brewers remained eligible to file for arbitration Thursday: first baseman Prince Fielder, right fielder Corey Hart, second baseman Rickie Weeks and right-hander Seth McClung.