Byce went to the University of Wisconsin where he did develop into a decent prospect. He was a two time all star in the WCHA. In his final season he scored 27 goals and 71 points in 46 games. In his collegiate career he scored 77 goals and 88 assists in 169 games, though his first 40 games in his rookie season hardly count as rookies generally warm the bench in their first season, as Byce did.
Following the completion of the collegiate season, Byce was asked to join the Bruins for the playoffs. Byce expected he would watch from the press box but was happy just to practice with the squad. However Byce appeared in 8 playoff games, injecting speed and enthusiasm into a veteran Bruins lineup that went all the way to the Finals to face the Edmonton Oilers. His NHL debut came in game 6 of the Bruins' Adams Division Semi-Finals series against the Whalers and scored his first NHL goal in game 7. He notched his second goal of the playoffs 10 seconds into game three of the finals, helping the Bruins to their only victory of the series. That goal tied a record for fastest goal at the start of a final series.
Despite the promise shown in the 1990 playoffs, Byce spent most of the next two seasons in the AHL with the Bruins' farm team. He appeared in 21 NHL games in those two seasons, scoring twice and adding three assists. On February 24, 1992, he and Dennis Smith were dealt to Washington for Brent Hughes. Byce never appeared with the Capitals or any other NHL team again.
Byce would go on to a lengthy minor league career as well as spending one season in Sweden. For a 220th overall draft pick, Byce defied the odds and had a long professional hockey career, and even appeared and impressed in the NHL.
Byce has had a lot of time to reflect on the whirlwind 1989-90 season.
"It all happened so fast. It was an incredible experience and it was totally unexpected. Obviously, to win a national championship and be able to play in the Stanley Cup Finals all in one year was pretty amazing. I even thought if you win the Stanley Cup you might as well retire because you’ve done everything already. After that year it got harder. I played a few NHL games but didn’t quite stick.
"Just remembering back, it was kind of a whirlwind at the beginning. You’re just so excited to be there and the intensity’s unbelievable. You have no problems getting ready for those games initially, but I remember after three or four games you settle in a little bit and then it becomes a little bit more of a grind throughout the playoffs. The difference is the intensity — the speed of the game picks up from what college was.
"It was an incredible opportunity but I honestly think two or three years into my professional career I was a better player than I was at the beginning when I got thrown into the fire. In the NHL, when you get that opportunity the first year or two and you don’t stick, it’s much harder to get back. And I think that’s what happened to me. I think if I would have spent some time in the minor leagues those first couple of years and develop a little bit, I think I was a better player two, three years later. I think if I would have got my shot at that point, I think I would have had a better opportunity to spend more time in the NHL."