single buzzy string

This is on a fretless 4 string with the generic factory installed strings.

E string has a buzz everywhere on the fretboard. The only way to prevent it is to pull the string down to the A string when holding the note. The buzz is coming from around the bridge I think (body of the guitar). The other strings play perfectly so I'm assuming the truss rod is good. Also the string height at the bridge is already above the height of the other strings and has the string positioned about 1/2" from the pickups.

Is this sounding like a stretched out string or is it sounding like the bridge may be needing some attention?