I actually struggled with this for hours and finally determined that my issue was that, because I am a Mac user, my default output is Preview. I could not get this to work until I installed Acrobat Reader on my Mac. As soon as I did this several methods worked for me.
Ultimately I used the layers method similar to what Tobias laid out. I created my entire document in InDesign and made sure that the full color background for screen was on one layer and my black and white elements for print purposes on a second layer.
Then I opened my interactive PDF in Acrobat Pro on my Mac and opened the Layers panel, right clicked the colored layer that I only wanted to show on screen and not print, and designated the full color background for screen only to "Never Prints" here.
I was having trouble getting this to work no matter what I did until I finally installed Acrobat Reader on my machine. Actually, it worked for Acrobat Pro as well, but most users are not going to have Acrobat Pro installed on their machines... and that was the clue that pointed me toward Acrobat Reader over Preview. The print version (B&W) showed up in my Print Preview pane (FINALLY!!) and it occurred to me that Preview could not "process" the layers in the Adobe created file (for lack of a better way to describe it).
Regardless, this is my solution, it works, this is what was causing me so many problems and how I overcame them... and I hope this helps others that are trying to do something similar using a Mac!