Bruce was a National High School Player of the year candidate in 2005. On average, Bruce had 30 scouts per game his senior year.
On August 1, 2016, Jay became the first player traded during the season while leading the league in RBI since the stat became official in 1920 when he was acquired by the New York Mets from the Cincinnati Reds. He finished the season with 33 home runs and 99 RBI, both the second-highest totals in his career. Jay made 1,072 career appearances in right field with the Reds, a franchise record for games at that position (surpassing Ival Goodman, 889 games in RF from 1935-42). A three-time National League All-Star, Jay is one of only six players in Reds franchise history with at least 1,000 hits and 200 home runs, joining Johnny Bench, Tony Perez, Frank Robinson, Ted Kluszewski and George Foster.
On May 28, 2008, Jay became the first major-league player to reach base in the first six plate appearances of his career.