A right-hander, Bolin was born in Hickory Grove, South Carolina, and was listed as 6 feet 4 inches (1.93 m) tall and 185 pounds (84 kg).

Bolin entered pro ball after signing with the New York Giants on November 10, 1956, at the age of 17 out of Rock Hill High School.

In 1968, Bolin had the second-best earned run average (ERA) in the National League, 1.99, behind only Bob Gibson's record-setting mark of 1.12.

Bolin finished in the NL's top ten three times for ERA, WHIP, and hit batsmen, and twice for shutouts, strikeouts per nine innings pitched, winning percentage and bases on balls allowed.

As a member of the 1962 National League champion Giants (for whom Bolin went 7–3 with six saves), he appeared in two games of the 1962 World Series against the New York Yankees, allowing four hits and two earned runs in 22⁄3 innings pitched.