Jazzy -
I would be VERY careful about using a rouge cloth on your inlay. When they assemble the inlay, it's all done by hand and there will be little rough edges and gaps where the pieces fit together. If you snag them with your rouge cloth, you may dislodge pieces of the inlay!
The safest thing to do is to not worry about the tarnish since it developed because you love your bass. I think jewelers have polishing sticks that are covered with microfiber cloth that you could use to polish particularly pieces of metal, but you still want to avoid rubbing the edges of the inlaid pieces.
My 2 cents,
David Fung