Betts was born William Thomas Betts in Port Chester, New York. His nickname was an abbreviation of "mosquito."

A drummer as a child, Betts took up the bass as a senior in high school. In 1949, he joined Earl Bostic's rhythm and blues band. Two years later, he met Washington when she sang with Bostic, and she invited him to become her full-time bassist.

Betts joined Byrd's group in the late 1950s; years later, he told a reporter than it was he who introduced the guitarist to Brazilian bossa nova, paving the way for the 1962 album Jazz Samba, an enormous hit.

In the mid-60s, Betts began to perform with singer Ella Fitzgerald. Their collaboration lasted until Fitzgerald retired from performing in 1993.

He also played with Oscar Peterson, Tommy Flanagan, Woody Herman, Nat Adderly, and others. Toward the end of his life, he released three albums under his own name.