As a boy, Bomar lived in Groesbeck, Texas where his father Jerry coached and was the ball boy for their State Championship team in 1991. Coached by his father at Grand Prairie High School who is now the athletic director and head coach of the high school football team in Beeville Texas. Bomar was a starter for three years. He was ranked as the nation's No. 1 high school quarterback of 2004 by the recruiting services Rivals.com and Scout.com and was compared to former NFL great John Elway. He threw for 1272 yards and rushed for 547 yards as a senior. Bomar committed to Oklahoma in February 2004. He played in the 2004 U.S. Army All-American Bowl. Bomar was an athletic director and the head coach of the football team at the Freer Early College High School, in Freer, Texas until March 2017. He currently holds the position of offensive coordinator at Alief Taylor High School in Houston, Texas. In the spring of 2017 it was announced that Bomar would follow former Alief Taylor defensive coordinator Cedric Hardeman to Conroe to become Hardeman’s offensive coordinator with the Tigers.
College career
Oklahoma
Bomar became the starter by the 2nd game 2005 season. His season started roughly while he adjusted to college football, but his game improved throughout the season. He was named the Most Valuable Player of the Holiday Bowl when Oklahoma defeated the Oregon Ducks. On August 2, 2006, Bomar was dismissed from the team by OU head coach Bob Stoops. It was reported that he was paid for work at Big Red Sports and Imports, a car dealership owned by a major University of Oklahoma donor, but that he did not complete the work, a violation of NCAA rules. Senior Paul Thompson began the year as starting quarterback, backed up by true freshman Sam Bradford and junior college transfer Joey Halzle.
Sam Houston State
Bomar entered spring practice as the starting quarterback for the 2007Bearkats, with two years of collegiate eligibility remaining. He played nine games the first year for the Bearkats before injuring his knee on November 3, 2007 against Nicholls State. “Rhett brings a lot of athleticism to the quarterback position that we haven’t had,” SHSU coach Todd Whitten told the Huntsville Item. “He's going to get a chance to get a lot of reps this spring. We feel like our offense has the chance to make a lot of big plays next year.” Bomar started all 10 games in 2008 for Sam Houston State as the Bearkats went 4-6 on the season. He completed his college career as Sam Houston's all-time leader in passing with 5,564 yards in 19 games and career leader in total offense with 6,159 yards. He was a two-time All-Southland Conference selection and ended the 2008 season ranked No. 2 in NCAA Division I Football Championship Subdivision total offense and No. 4 in passing offense. Bomar passed for more than 300 yards in nine games during his Bearkat career. He threw for passes of more than 50 yards 10 times, including his longest of 80 yards. He is one of only 11 players in NCAA FCS history to throw for more than 300 yards and rush for more than 100 yards in a single game. He was also selected as a finalist for the Walter Payton Award given to the top player in the Football Championship Subdivision.
Professional career
New York Giants
In the 2009 NFL Draft, Bomar was drafted by the New York Giants as the 15th pick of the 5th round. Bomar on June 24, 2009 signed a four-year contract, including a $185,183 signing bonus. He was waived on September 5, 2009, and re-signed to the practice squad on September 6. Bomar was promoted to the active roster on December 31, 2009. On September 4, 2010, Bomar was waived by the Giants. Following an injury to Giants quarterback Jim Sorgi, Bomar was initially expected to take over the role as backup quarterback, but on September 3, 2010, the Giants acquired Sage Rosenfels from the Minnesota Vikings to step in at the position, making Bomar expendable. On the following day, September 5, the Giants re-signed Bomar to the team's practice squad.
Minnesota Vikings
Bomar was signed by the Minnesota Vikings off of the Giants' practice squad on December 21, 2010, and made him the team's third-string quarterback for the final two games of the season.
Oakland Raiders
On January 6, 2012, Bomar was signed by the Oakland Raiders to reserve/future contract. He was waived May 14, 2012, following the Raiders' acquisition of Matt Leinart.