Hi Victoria and welcome to the forum! 
I don’t believe there is a way to print color from Asana. I think their focus is on the digital experience. Depending on what you are hoping to achieve with the printed version, you could take a screenshot of the board and print the screenshot. That would give you a printed copy of exactly what you are seeing on the screen. If that doesn’t suit your needs, you could try the integration Asana2Go which has some report printing capabilities.
I hope this helps,
Katie