Bass attended Trenton High School and Wayne State University. As a junior at Wayne State, Bass was named the 2008 Great Lakes Intercollegiate Athletic Conference Pitcher of the Year. He was the highest MLB draft pick in Wayne State history.
Bass was drafted by the San Diego Padres in the fifth round of the 2008 Major League Baseball Draft. He worked as a starting pitcher for the Single-A Fort Wayne TinCaps and Advanced-A Lake Elsinore Storm in 2009, and again for Lake Elsinore in 2010. He began 2011 with the Double-A San Antonio Missions, and although he made a single start for the Triple-A Tucson Padres in May, he was promoted to the big leagues from Double-A in June.
Bass made his major league debut on June 13, 2011, pitching a five-inning start and earning his first major league win. He was optioned back to San Antonio the next day, but was recalled again in late June. Bass stayed with the big league club for the remainder of the year, pitching out of the bullpen until making two more starts in late September. He finished 2011 with a 1.68 ERA in 48 1⁄3 innings and 24 strike-outs versus 21 walks.
Bass started 2012 in the Padres bullpen, but was added to the starting rotation on April 12 when Dustin Moseley injured his shoulder. Bass made 14 starts for the club until he went on the disabled list in June with shoulder inflammation. He rejoined the club in September, working out of the bullpen after making three rehab starts with Tucson. Bass finished 2012 with a 2-8 record and a 4.73 ERA in 97 innings, with 80 strike-outs against 39 walks.
On December 11, 2013, Bass, along with a player to be named later or cash considerations, was traded to the Houston Astros for a player to be named later or cash considerations. The Astros sent Patrick Schuster to the Padres the next day. Bass spent the 2014 season split between the Astros and the team's Class AAA affiliate, the Oklahoma City RedHawks. He appeared in 21 major league games and earned two saves. He was outrighted off the Astros roster on November 20, 2014. On December 6, Bass elected free agency.
Bass signed a minor league deal with the Texas Rangers on December 11, 2014.
After the 2015 season, the Rangers traded Bass and Leonys Martín to the Seattle Mariners for Tom Wilhelmsen, James Jones, and a player to be named later (Patrick Kivlehan).
Bass was released by the Mariners on January 7, 2016 and signed with the Hokkaido Nippon-Ham Fighters on January 8. Bass earned three wins during the 2016 Japan Series to lead the Fighters to victory in the championship series, including the fourth win for the team to clinch the team's fifth championship.
Bass signed a minor league deal with the Texas Rangers in February 2017..
He throws four pitches: a four-seam fastball (90–95 mph), a slider (83–87), a cutter (85–87)and a changeup (82–86). Bass throws all three pitches to right-handers and left-handers, but he uses the slider more against right-handed batters and the changeup more against lefties. He favors the slider with two strikes.
On January 27, 2017, Bass married Sydney Rae James, sister of country singer Jessie James and sister in-law of New York Jets Wide Receiver Eric Decker. They welcomed a Baby Girl named Brooklyn Rae on September 4, 2017.