Bluege batted .272 in his career, but was chiefly known for his defensive ability, leading American League third basemen in double plays in three different seasons. His moonlighting job earned him the nickname "The Accountant" from teammates. Bluege's only All-Star appearance, in 1935, came in a year which saw him primarily play shortstop for Washington.
After retiring in 1939, Bluege managed in the minors for four years before taking over the Senators from 1943 to 1947. He compiled a career managerial record of 379-394, with two second-place finishes. In 1948, Bluege was named the Senators' farm director, where his greatest scouting coup was a young Harmon Killebrew. In 1958 he became the team's comptroller, shortly before its relocation to Minneapolis as the Minnesota Twins. He remained the team's comptroller until his retirement in 1971, having served the organization for 50 years.