Grove Music lists this piece as being for 2 double basses and piano, and the entry is: "Passione amorose, 2 db, pf [from Concerto di bravura]". IMSLP does not currently have the Concerto di Bravura, which was for a single double bass and piano, so it is not possible to say how distinct this version is. In the meantime, it should probably stay on its own page as a distinct piece, although in the future, it may be moved to the "Arrangements and transcriptions" tab of the parent piece.
Grove Music does not list the orchestral version, so it is unclear who did that version, but it is not original to Bottesini.
This music is an arrangement of one of the songs from G. Rossini's "Les soirées musicales".