For what it's worth, I'll offer my opinion as if it were my bass. If you are considering a natural finish, you might have to play it by ear as you remove the paint. Sometimes lower quality woods are used in factory painted basses. Also, any gouges, deep scratches etc or glue joints in the wood will effect the look of the bass when a natural finish is desired. So be prepared to change strategy if these things pop up after the paint is removed.
As far as paint removal is concerned, I would take everything off the body and go with a chemical process. It's a messy job that requires proper ventilation. Any commercial paint stripper, say from your Home Depot, etc would do. I would not sand the paint off because you might wind up sanding some of the character lines, radii down on the body. You might have to do the stripper a few times, then fine sand to get to a smooth finish. Be patient with the stripping process-read the directions and let the chemicals do thier thing. If you want to, you could see if there is a local paint stripper in your area who can dip the body-probably the best solution. Once the body is naked, you can evaluate the type of wood, grain and condition to determine whether the body is fit for a natural finish or not.