Bamboo Cutting board I recently purchased a bamboo cutting board and it's shedding fine splinters of wood.  Is there a way to clean this off or did I buy a bad quality board?  

I've tried washing it but water doesn't seem to rinse off the fine splinters of wood very well.  In fact, the water makes the fine splinters of wood stick!
It sounds like the one you got may not have been of good quality. I don't remember them being terribly expensive ($40?), so I'd take yours back. If you get a good one, it should last you for years and years, so don't be afraid to invest a little. Your new one should NOT be splintering. 

And don't put your new one in the dishwasher.