He signed with the New York Giants out of high school, under the agreement that he could earn his degree at Dartmouth College while pitching in their minor league system.

After a stint in the United States Army, Burnside made his major league debut in 1955, picking up his first win the same year and impressing Carl Hubbell, Giants' Hall of Fame pitcher and farm director.

He was traded to the Baltimore Orioles after the season, started 1963 in their bullpen, and was reacquired by the Senators following his release in May; however, he had a 6.15 earned run average for Washington.

He went to Japan following the season, pitching two years with the Hanshin Tigers of Nippon Professional Baseball before returning to Illinois to become a teacher and coach at New Trier High School, his alma mater.

His father Robert, a salesman, married his mother, the former Helen Willits, six years before Burnside's birth—the couple separated in the early 1930s.

Chub Feeney, the Giants' president, was a graduate of Dartmouth and worked out an agreement with Burnside under which the pitcher could wait until the spring semester was over to begin his seasons, allowing him to earn his degree.

[1] In 1950, he appeared in 12 games with the team, going 2–6 but posting a 10.07 earned run average (ERA), the product of 60 walks in only 42 innings of work.

[1] In nine games for Nashville, he had a 2–3 record and a 4.90 ERA—and then, with the Korean War going on, Burnside was drafted into the United States Army Medical Corps, ending his season.

“[Burnside] ha[s] the stuff, in bountiful quantity...it’s only a question of polish and control before [he] is ready to wear [a] Giants uniform” opined Joe King of the Sporting News.

[1] Burnside continued to hone his skills in winter ball, joining Giants' stars Willie Mays and Rubén Gómez in helping the Cangrejeros de Santurce win a pennant.

“I want a chance to pitch regularly and I know I’ll get it here.”[1] His 1955 season in the Class AA Texas League, where he posted an 18–11 record, a 2.47 ERA, and a league-leading 235 strikeouts for the pennant-winning Dallas Eagles, earned him his first big-league call-up to the New York Giants in September.

[1] He got his second (and last) victory in a Giant uniform April 23, when he threw a complete game, three-hit shutout to defeat the Pirates 1–0 at the Polo Grounds.

[6] He failed to get through the inning in three of his next four starts, then got sent to Minneapolis in May, though he was called up at the end of the month when the Giants hit a stretch of 15 games in 13 days.

[7] While Burnside did not have a great spring training in 1958, he was added to the Giants' first San Francisco roster because the team did not wish to expose him to waivers.

[8] That day, he entered a game against the Milwaukee Braves that the Giants led 7–4 with two outs in the ninth; Burnside relinquished a game-tying home run to Wes Covington in an eventual 10–9 loss.

Several times he’s been on the verge of establishing himself in the major leagues.”[1] Burnside entered 1959 with another new pitch, a screwball, which he had learned from teammate Marv Grissom in 1958 and practiced in winter ball over the offseason.

[7] The American League expanded to 10 teams after the season, and the Tigers left Burnside unprotected for the expansion draft, allowing the Washington Senators to take him with the eighth overall pick.

“When he had those good days late in the season, there was not a better pitcher in the league.”[1] In 33 games (16 starts), Burnside had a 4–9 record, a 4.53 ERA, ad 56 strikeouts in 113+1⁄3 innings pitched.

[1] On April 14, 1962, Burnside limited the Indians to four hits and two runs in a 5–2 victory, pitching a complete game that only lasted five innings because of rain.

[7] On December 5, he and Bob Johnson were traded to the Baltimore Orioles for Marv Breeding, Art Quirk, and Barry Shetrone.

[7] The Houston Colt .45's offered him a tryout, but Burnside re-signed with Washington on May 24, replacing Quirk (a pitcher), who had just been optioned to the minor leagues.

[1] During his eight-season MLB career, Burnside lost 36 of 55 decisions (for a winning percentage of .345), and in 5671⁄3 innings pitched he surrendered 607 hits and 230 bases on balls; he fanned 303.

Following his baseball career, Burnside obtained his master's degree from Northwestern University, then returned to his high school alma mater, New Trier, where he was a teacher and coach from 1967 through 1993, when he retired.