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Double Bass here's a stupid question...

In most jazz, the assumption is that each player knows how to create his/her own part. An experienced jazz guitarist can improvise an appropriate accompaniment given a set of chord changes and a general style or "feel."

What is the music in question? Your own compositions, something out of a Real Book, ?
 
Guitar often plays rhythm when you're melody-ing. It can be as simple as one whole note chord played per bar, or a more complex rhythm based on the melody - sort of like what you do when you accompany someone else, only with chords.