Billings is the son of Bruce and Emily. Billings attended the San Diego School of Creative and Performing Arts (SDSCPA) and Samuel F. B. Morse High School and San Diego State University who played for the SDSU baseball team as a short reliever in 2004 and a starter in 2005 and 2006. Billings was drafted by the Philadelphia Phillies in the 2006 MLB June Amateur Draft in the 31st round, but decided to stay one more year at San Diego State. Billings was again drafted by the Colorado Rockies in the 30th round in the 2007 MLB June Amateur Draft, 912th overall, and he accepted the deal.
Billings started his minor league career with the Tri-City Dust Devils where he went 4-2 in 15 starts. In 2008 with the Asheville Tourists, Billings threw a no-hitter against the Lakewood BlueClaws. Billings started to convert to a reliever in 2010 with Tulsa with more than half of his appearances being in relief. Billings was also a mid-season All Star with Tulsa. Billings did not pitch one start in 2011 with Colorado Springs before being promoted.
On May 25, 2011, Billings was recalled to the majors when Jorge de la Rosa being placed on the 15-day disabled list with a tear of the ulnar collateral ligament in his left elbow.
On May 27, Billings made his major league debut in relief of Matt Daley. Billings pitched the 8th and the 9th innings in a 10-3 loss to the St. Louis Cardinals, giving up 5 hits and 1 run, while recording no strikeouts.
Billings and a player to be named later were traded to the Oakland Athletics for Mark Ellis on June 30, 2011. He pitched five innings in three games for the Athletics, allowing seven runs. He spent the next two seasons with the Sacramento River Cats in AAA.
Billings signed a minor league deal with the New York Yankees in December 2013. He appeared in five games for the AAA Scranton/Wilkes-Barre RailRiders and one for the Yankees, where he allowed four runs in four innings. He was designated for assignment on July 22, 2014. He was released on August 2.
On August 7, 2014, he signed a minor league contract with the Los Angeles Dodgers and reported to the AAA Albuquerque Isotopes. He appeared in five games for the Isotopes, all as a relief pitcher and was 1-1 with a 6.75 ERA. He became a free agent at the end of the 2014 season.
On November 21, 2014, the Washington Nationals signed Billings to a minor league deal with an invitation to spring training. He elected free agency on November 6, 2015.
In February 2016, he signed with the Uni-President 7-Eleven Lions, a professional baseball team based in Taiwan. He joined the spring training in the mid-February with a former MLB players, Felix Pie, and Jair Jurrjens.