William Correa was born on February 28, 1934, in New York City to a Puerto Rican family and grew up in Spanish Harlem. His father played the cuatro, the ten-string Puerto Rican guitar, and the boy taught himself bongos, then congas, timbales and drum set. According to Wikipedia he was dancing professionally at twelve and made his first recording, on bongos, two years later. From 1947 he worked as a band boy for Machito's Afro-Cubans, which got him through the door at their engagements and sometimes onto the bandstand to fill in on percussion. He soon met Mongo Santamaría, newly arrived from Havana, and studied with him while acting as his translator; he also learned from the conga player Armando Peraza. AllMusic adds that he was playing with the bandleader Pérez Prado at fifteen. In June 1951 he played bongos on a Circle single by Mary Lou Williams, "Handy Eyes" and "S'Posin'," and she is said to have given him the nickname Bobo.

From 1954 to 1957 he sat in the percussion section of Tito Puente's orchestra beside Santamaría, who had talked Puente into hiring him. He is heard on Puente's Puente in Percussion (Tico, 1956) and Top Percussion (RCA Victor, 1958) and, according to Wikipedia, on Cuban Carnival (RCA Victor, 1956). While still with Puente he played on The Shearing Spell, the first Capitol album by the pianist George Shearing, after Peraza introduced him to the group. Bobo and Santamaría then joined the vibraphonist Cal Tjader's group in California, where Bobo stayed from 1958 to 1961 and recorded Latino (1958) and the live Concert by the Sea, taped in Carmel in 1959. In 1960 Santamaría took him to Havana to record two albums, Mongo in Havana and Our Man in Havana, and the two reunited on Sabroso! for Fantasy.

Back in New York he began recording under his own name, with Teddy Reig producing: Bobo! Do That Thing/Guajira for Tico (1963), then Bobo's Beat (1963) and Let's Go Bobo! (1964) for Roulette. AllMusic names Clark Terry and Joe Farrell as sidemen on the first of these. In 1963 his working band included Chick Corea, Farrell and the teenage trumpeter Woody Shaw. He was also one of the busiest percussionists in the city, on Grant Green's The Latin Bit (recorded 1962), Sonny Stitt's Stitt Goes Latin (1963), Herbie Hancock's Inventions and Dimensions (recorded August 30, 1963, with Bobo on drums and timbales), Wes Montgomery's Movin' Wes (recorded November 1964), three Impulse! albums with Chico Hamilton in 1965 and 1966, and a run of dates for Herbie Mann between 1962 and 1967. Wikipedia credits him with bongos on Miles Davis's Quiet Nights (1963), the unfinished album of Gil Evans arrangements, and on "Nothing Like You," a 1962 session later placed on Sorcerer (1967).

He returned to Tjader for Soul Sauce, recorded in New York in November 1964. His shouted call-outs are part of the title track's sound, and, according to Tjader's biography, the album's name grew out of a suggestion from the producer Creed Taylor and a remark of Bobo's that Tjader's version was spicier than the original. Verve then signed him as a leader. Spanish Grease, cut in 1965 at Rudy Van Gelder's studio in Englewood Cliffs, New Jersey, reached No. 137 on Billboard's album chart in 1966, and its title track, written by Bobo and the cornetist Melvin Lastie, became his signature tune. Further Verve albums followed: Uno Dos Tres 1-2-3 and Feelin' So Good (both 1966), Juicy and Bobo Motion (both 1967), Spanish Blues Band (1968) and A New Dimension (1969), followed by the compilation Evil Ways (1968). They set pop and soul hits, Brazilian songs and boogaloo originals to Latin rhythm with an electric guitar in place of the usual piano. "Evil Ways," written by his guitarist Clarence "Sonny" Henry, was first recorded for Bobo Motion in July 1967; Santana covered it on their 1969 debut album and took it to No. 9 on the Billboard Hot 100. "Fried Neck Bones and Some Home Fries," which Bobo wrote with Lastie for Uno Dos Tres, was played by Santana at Woodstock in 1969.

He moved to Los Angeles in 1969, led jazz and Latin jazz combos, worked as a session musician for Carlos Santana and others, and played in the band for Bill Cosby's 1976 variety show Cos. With his group the Bo-Gents he recorded Do What You Want to Do for Sussex (1971). In 1975 he joined Louie Bellson, Shelly Manne and Paul Humphrey for the drum-summit album The Drum Session, and he later made Tomorrow Is Here for Blue Note (1977) and Hell of an Act to Follow (1978) and Bobo (1979) for Columbia. In 1983, about three months before his death, he shared the stage with Santamaría at the Playboy Jazz Festival, their first reunion in fifteen years, according to AllMusic. Bobo died of cancer in Los Angeles on September 15, 1983, at the age of 49. His youngest son Eric Bobo, a percussionist with Cypress Hill who also played on the Beastie Boys' Ill Communication (1994), later brought out Lost & Found (Concord Picante, 2006) and Dig My Feeling (Nacional, 2016), both drawn from his father's unreleased recordings of the 1970s.

Bobo came up through the Afro-Cuban tradition of Machito, Puente and Santamaría and carried its timbale and conga vocabulary into jazz rhythm sections, where he could also play a swinging drum set; Wikipedia notes that he rejected the stereotyped role of the Latin percussionist and moved easily among jazz, Latin and rhythm and blues. AllMusic describes a relentless swinger and flamboyant showman who was also an engaging, if modestly gifted, singer, and says his favorite song was Antonio Carlos Jobim's "Dindi." His son Eric has said that he did not read or write music. In the mid-1960s he became one of the pioneers of the boogaloo, or Latin soul, style, covering the pop and R&B hits of the day over Afro-Cuban rhythm. Jazz critics of the time often dismissed those Verve albums, and reissues and hip-hop samplers later restored their reputation; "Spanish Grease" remains his best-known tune, and Santana's version of "Evil Ways" carried his repertoire to a far larger audience. His audience therefore straddles Latin jazz, soul jazz and dance-floor music, but the work that frames his career is jazz: the Tjader and Santamaría groups, the Latin dates for Grant Green and Sonny Stitt, and the Blue Note and Columbia albums of the late 1970s.