Both cork and bamboo are very sustainable resources, but cork flooring is a recycled by-product from the production of other cork products, making it more eco-friendly than bamboo. Cork is probably the more "green" option, mostly because of the harvesting process, which keeps forests alive and healthy, and does not require the cutting down of trees to get the material. In fact there are laws in place protecting cork forests from harvest until they reach a certain age and size, which means that keeping the forest healthy for many generations is a priority, and more profitable for manufacturers.
However, there are a LOT of differences in feel as well as in appearance between bamboo and cork flooring, and they should be taken into consideration for your application- but if your main concern is the environment, then cork would be my suggestion, based purely on sustainability.
'Green' as a label unfortunately is not that clear cut. When talking about a green product it is not just the material (bamboo or cork) but also the production method and possible chemicals involved in the production, transportation (the closer it is fabricated and grown, the greener the product) and life span and possible recycling options. All of the above are facts that vary from brand to brand, and it is best to ask your flooring company specific questions about teh product you are considering to put in your house.
Both cork and bamboo are considered 'green' products: They are renewable, but bamboo for instance used to have high VOC (Volatile Organic Compound) readings, a fact that has been improved during the past few years.
When considering flooring it also depends on what you are looking for. Bamboo is very hard and durable, but it doesn't dampen noise and can be hard on your feet when you are standing in one spot over an extended period of time. Cork is soft and counteracts echo-y rooms, it's easy on your feet, but it fades in sun exposed areas.