Hey Lewis!
This is an awesome question. So I think that managers need to understand the value of using and creating open source projects. A huge part of that is the end result will be better. Just one example is bugs will be found by other developers rather than your users.
I think that business users can see the value better if they see $$$ attached to it. So let's say you have a situation where a library is almost what you need except for some bug or something. So you can say this:
Hey, listen, so this open source software is almost just what we need except for this one thing. So I can either spend a day contributing back, or I can spend 6 weeks building a less-good version myself. What would you like me to do?
Try to bring things back to money/time/etc. Also, I think more of the world is starting to embrace open source. So it really is often just a matter of asking. Good luck!