Bliss was born and raised in Binghamton, New York and graduated from Binghamton Central High School in 1961. He graduated from Cornell University in 1965 where he was elected to the Sphinx Head Society. He then earned an MBA from Cornell in 1967. He was an all-Ivy League guard at Cornell, was captain of the baseball team, and was named to the first team Eastern Intercollegiate Baseball League in 1965. Bliss was inducted to Cornell’s athletic Hall of Fame in 1984.

From 1980–88, Bliss was the head coach at Southern Methodist University. He led the Mustangs to three NCAA tournaments, in 1984, 1985 and 1988. His best season was the 1987–88 season, in which the Mustangs won their first outright Southwest Conference regular-season title in 21 years and won the Southwest Conference tournament.

One of Bliss’s most successful players while at SMU was Jon Koncak, who was the fifth overall pick in the 1985 NBA Draft by the Atlanta Hawks and gold medalist on the 1984 U.S. Olympic basketball team coached by Knight. An NCAA investigation during the mid-’80s reported that Bliss was involved in payments to his players, including Koncak, in violation of NCAA rules. But the NCAA chose not to pursue the investigation any further due to the football program having received the “death penalty”. Koncak told the Fort Worth Star-Telegram that he received payments while at SMU, in violation of NCAA rules:

Baylor University hired Bliss as head coach for Baylor Bears basketball on March 23, 1999.

After a memorial service for Dennehy in San Jose, California, Bliss asked to meet with school investigators. At that meeting, he was told that Dennehy’s girlfriend had told them Bliss paid for the sections of Dennehy and Herring’s tuition not covered by financial aid. Bliss confessed to making the payments, estimated at $7,000—a major violation of NCAA rules. Two members of Baylor’s 2001–02 squad told the Dallas Morning News that Bliss and several members of his staff had been present at a pickup game involving star recruit Harvey Thomas during his official visit to Baylor—another major NCAA rules violation. It also emerged that Bliss and his staff knew about rampant marijuana and alcohol abuse among Baylor players, but did not follow procedures for reporting failed drug tests. Under the circumstances, Bliss was forced to resign on August 8, 2003.

In 2005, Bliss was given a 10-year show-cause order for what the NCAA called “a blatant and sweeping disregard” of NCAA rules. If he had been hired by an NCAA member school in an athletic capacity before the penalty had expired in 2015 (he hadn’t been hired), Bliss would have had to agree to abide by any restrictions the NCAA infractions committee imposed on him, and then report back to the NCAA in writing every six months for the duration of the order or until the end of his employment. Bliss’s prospective employer would have had to show cause for why Bliss would not have to have restrictions imposed on his duties. The penalty is the most severe punishment the NCAA can hand a coach. Ash was hit with a five-year show-cause order. Another assistant, Rodney Belcher, was hit with a seven-year show-cause order for lying about recruiting violations committed in the course of bringing Dennehy to Baylor.

Bliss served for two years as a volunteer assistant coach at a Denver-area high school before being hired as head coach of the Continental Basketball Association’s Dakota Wizards. He only lasted one season as coach of the Dakota Wizards before resigning, citing family reasons. In 2008, he returned to Texas for several speaking arrangements, including a Baptist church sermon and the annual convention of the Texas High School Coaches Association.

In May 2010, Bliss became dean of students, athletic director and head men’s basketball coach at Allen Academy, a college preparatory school in Bryan, Texas.

Almost immediately Bliss became embroiled in controversy. On November 28, 2010 it was reported by multiple news outlets in Bryan that Bliss received a two-year suspension from coaching basketball and a one-year suspension from school administration at Allen Academy by the Texas Association of Private and Parochial Schools (TAPPS), the largest athletic governing body of private schools in Texas. The suspension came less than a month after the start of his first season as head boys’ basketball coach and less than three months after joining the school in an administrative role.

In 2015, Bliss was hired as the head coach at NAIA-member school Southwestern Christian University. Bliss resigned from Southwestern Christian on April 3, 2017, following the airing of the Showtime documentary Disgraced, which chronicled the cover-up at Baylor.

In 2017, a Las Vegas high school hired him as their head coach. Bliss resigned in 2018, after one season as head coach.