Is your bamboo cup BPA approved? The majority of reusable cups used by coffee drinkers are either plastic or bamboo. Always read the label when buying bamboo as they are not all biodegradable due to an added plastic resin that bonds together the bamboo. If a product does not contain a BPA trademark, simply look for alternative brands. Companies such a "ecoffee cup" are all BPA free and guarantee the cup, lid and sleeve to be fully biodegradable, yet retaining the original taste of the coffee.
Many coffee shops have started to offer discounts for those who bring in their own reusable cup. A great way to reduce waste but also reduce plastic waste which seems to be dumped into the sea, effecting wildlife, often life threatening.
There are many inventors targeting this area as ethics seems to be major part of building awareness, however, make sure you still do your homework to ensure the cups are fully biodegradable or recycle, otherwise whats the point?