Ore attended the New School of Music in Philadelphia from 1943 to 1946, studying cello, and followed this with studies on bass at Juilliard.
In the 1950s he worked with Tiny Grimes, George Wallington, Lester Young, Ben Webster, Coleman Hawkins, Elmo Hope, Bud Powell and Freddie Redd. From 1960 to 1963 he played in Thelonious Monk's quartet, and then with the Les Double Six of Paris in 1964. Later in the 1960s he played again with Powell and also recorded with Teddy Wilson. In the 1970s he worked with Earl Hines. He was with the Sun Ra Arkestra in 1982. Following this he became less active and never recorded an album as a leader.