Born in Lawrence, Kansas and a distant relative of New York Yankees' Tommy Henrich, Bobby first attracted the attention of pro scouts following his junior year at Compton High School.

He ran the 100-yard dash in 9.7 seconds, and also played football and basketball in high school before concentrating on baseball his senior year.

The Cincinnati Redlegs got a jump on the other clubs, though, by signing Bobby's father Ed, a junior college coach, as a scout.

During the winter, Henrich went to South America and played in the Panamanian League during three seasons, helping the Carta Vieja Yankees club win the 1954–1955 pennant.

With the repeal of the bonus rule, Henrich was allowed to be optioned to the minors in 1958, spending the season with the Savannah Sand Gnats in the South Atlantic League, while playing third base.