For exterior bronze:
Mechancial polishing using jewelers rouge and a high speed buffing
wheel, followed by several heavy coats of 2-part (catalyzed)
acrylic/urethane clear. For me this lasts about 2-1/2 years - if the
coating remains intact. When the coating eventually fails, simple
paste type paint remover will lift the acrylic/urethane ... a light
power-buff and recoat is all thats needed for another 30 months.

If you use 'chemical' polishes you must totally remove them before
coating, etc.
Dont bother with spray-on clear urethane or clear lacquer as its too
air/water vapor permeable and will allow re-tarnish in a ust few
months.

Otherwise..... rub on a mixture of lime juice, beeswax and olive oil
..... will turn the bronze to a golden brown and will prevent the
'green' from forming. The 'ancients' used this formula to coat their
bronze; when they needed to 'burnish' or polish they simply added fine
pumice to the mix and rubbed hell out it.