Wow! Very nice job on the photo attachment, Matt...and a self-portrait in the bell as well!
As for polishing, my favorite of all is Blue Magic metal polish:
http://bluemagicusa.com/index.php/blue_magic/products/96/blue_magic_metal_polish_cream/http://bluemagicusa.com/index.php/blue_magic/products/94/blue_magic_liquid_metal_polish_8_oz/It is largely non-abrasive, and also works well for removing scratches on clear plastic lenses. After polishing, it leaves a protective coating to protect from tarnishing. The MSDS (Materials Safety Data Sheet) for it shows it to be largely harmless as such things go: Kerosene, non-fibrous aluminum oxide, fatty acid and ammonium hydroxide. Amazon carry it, of course:
http://www.amazon.com/BlueMagic-400-Metal-Polish-Cream/dp/B000BO8Z9IA lot of people use and prefer Brasso (
http://en.wikipedia.org/wiki/Brasso ) or Happich Simichrome polish (
http://www.simichrome-polish.com/ ). I know a number of people who have had good results using various automotive polished and waxes. One I know did well was Turtle Wax Chrome Polish and rust remover. It contains what amounts to solvents, silicones, water and fine abrasives. Nu-Finish car polish works well also.
Your pretty brass bell is really an alloy of zinc and copper, which are reactive metals. A lot of commercial and decorative brass is coated with lacquer to shield it from air and prevent corrosion, so many brass items stay nice for a long time...until the lacquer breaks down or wears off. If you're dealing with uncoated brass, then -- yes -- it has to be polished if it is to stay nice and not corrode.
Most commercial brass polishes -- Brasso comes to mind, as does Simichrome polish -- (and their inexpensive homegrown alternatives) tend to be either acidic, abrasive, or some combination of the two, and incorporate a protective component to prevent re-corrosion. If you're really after "cheap", there's lots of DIY methods, all of which might alter the appearance of your brass bell. Among the methods I've seen or heard...
• Rubbing with tomato catsup (ketchup) -- or tomato chutney, precursor to ketchup. (acid)
• Vinegar/salt/flour paste (acid, abrasive). I have seen this cause pitting.
• Water/salt/white vinegar mix. (acid)
• Lemon juice. (acid)
Matt, the homegrown products will get your brass shinier, but they can also cause scratches or pitting, and leave no protection behind to prevent corrosion. In fact, being unprotected, the brass may corrode even faster. For these reasons, I'd strongly suggest buying a small tube of a commercial polish like Brasso and using that to keep the bell looking pretty. It is a real beauty, and it would be a shame to have it damaged in some way while trying to keep it nice. By the way, the engraving looks especially nice!
Hope this helps.
All the best,
Dan.