Hey Chris, binding on the side of the fingerboard will look cool and should make the gap to side of the neck much less.
Make sure the binding is wider than the thickness of the fingerboard.
Have you thought about fret dot markers, they will have to go either in the top of the fingerboard or side of the neck. Depends which face will be more visible to the player, thinking the fretboard may be easier to see as the player leans over the bass