Be very careful with polishing Bakelite. (The antique radio collectors get into fits over this topic.) It is very possible to polish through the hard surface and get into porous substrate that will not polish to a shine. If I were you, I would use a plastic cleaner to get the Bakelite clean, use a plastic polish sparingly, and then use a nice automotive wax. The wax will restore some shine and depth of color to the Bakelite. (Note, some of the plastic collectors hate this and would consider waxing Bakelite heresy, but this piece is already less than pristine so I don't see how this makes it any worse than it already is.)
Good luck!