What are bars of music before the main theme called?

The term used for the bars of music that come before the main theme is "introduction." An introduction serves to set the stage for the main theme by providing context, establishing mood, or outlining the key. It often includes thematic material or motifs that may recur later in the piece, effectively preparing the listener for what is to follow.

The other terms listed are used in different contexts within music. "Inversion" typically refers to the rearrangement of notes in a chord or a melodic line, altering its harmonic structure. A "phrase" is a musical unit similar to a sentence in language, typically containing a complete thought within the music. A "transition" serves as a bridge between distinct sections of a composition, helping to ease the progression from one theme or idea to another. Each of these terms has its distinct function, but none represents the concept of the bars preceding the main theme as accurately as "introduction."