Answer by taking a quote from the following article:

Timmons was born in Philadelphia, Pennsylvania, the son of a minister. He had a sister, Eleanor. Both of his parents, and several aunts and uncles, played the piano. From an early age Timmons studied music with an uncle, Robert Habershaw, who also taught McCoy Tyner.

Timmons moved to New York in 1954. He played with Kenny Dorham in 1956, making his recording debut with the trumpeter in a live set in May of that year. He went on to play and record with Chet Baker in 1956-57 (bassist Scott LaFaro was part of this band for a time), Sonny Stitt in 1957, and Maynard Ferguson in 1957-58. He also recorded as a sideman with hornmen Curtis Fuller, Hank Mobley, and Lee Morgan, all for Blue Note Records in 1957.  Timmons became best known as a member of Art Blakey's band the Jazz Messengers, which he was first part of from July 1958 to September 1959, including for a tour of Europe. He was recruited for the Messengers by saxophonist Benny Golson, who said that "He was inventive, [...] He could play bebop and he could play funky - he could play a lot of things, and I thought it was the element that Art needed. He hadn't had anybody quite like Bobby, who could go here or go there, rather than walking in a single corridor." By late 1958 Timmons was sharing bandmate Morgan's East Sixth Street apartment and the pair had bought a piano, allowing Timmons to practice and Morgan to work on composing. From around the time he joined Blakey, Timmons, along with some of his fellow band members, was a heroin user. After leaving Blakey, Timmons joined Cannonball Adderley's band, in October 1959.  Timmons was also known as a composer during this period: The Encyclopedia of Jazz states that his compositions "Moanin'" (from the 1958 album of the same title), "This Here", and "Dat Dere" "helped generate the gospel-tinged 'soul jazz' style of [the] late '50s and early '60s." The first was written when Timmons was first with Blakey; the others were composed when he was with Adderley. "This Here" (sometimes "Dis Here") was a surprise commercial success for Adderley: recorded in concert in 1959, it was released as part of The Cannonball Adderley Quintet in San Francisco album while the band was still on tour, and they discovered its popularity only when they arrived back in New York and found crowds outside the Village Gate, where they were due to play.  Timmons was reported to be dissatisfied with the money he had received from "This Here", and was enticed in February 1960 into leaving Adderley and returning to Blakey's band by the offer of more pay. Timmons then appeared on further well-known albums with the drummer, including A Night in Tunisia, The Freedom Rider and The Witch Doctor. His own recording debut as sole leader was This Here Is Bobby Timmons in 1960, which contained his first versions of his best-known compositions. In the same year, he played on recordings led by Nat Adderley, Arnett Cobb, and Johnny Griffin, among others; on the first of these, Work Song, Timmons did not appear on all of the tracks, because he had been drinking heavily.

Who else did he play with at that time?
After leaving Blakey, Timmons joined Cannonball Adderley's band, in October 1959.