Yes, it oxidizes, tarnishes, over time - just like any other metal including Silver and Gold!
Metal reacting with the skin varies from person to person, and it is said that this is based on the pH level of your body (I have heard the more meat you eat the more likely your metals will tarnish) and of course how much you sweat will determine if metal turns green when you wear it. Humidity can also affect how much it oxidizes.From my experience it does not however turn clothes green.
It is said that like copper and brass you should not go in the shower wearing your bronze pieces as it is said that this can also turn your skin green, and can tarnish. However, I have to say I have worn mine in the shower and it has not done this to my skin, and I always take care to make sure to dry my jewellery after, this helps.
However, on the whole I would advise taking Elizabeth's pieces off whilst showering, washing up, playing sports and sleeping to aid in their longitivity.