Take control of your projects and make it easy for others to respond quickly to your requests by phrasing them as a yes or no question. This method keeps others' busy schedules from cutting into your productivity.
Image from qwrrty
Just like asking a busy person for a short meeting makes them more likely to fit you in, framing your requests in a way that allows them to make a fast decision (or respond without waiting until they get back to a computer) means they're more likely to actually get back to you.
This might mean more work on your end -- like proposing specific ways to partner with them right off the bat. You can always get their input once you've gotten in the door with their initial response and interest. For more tips on how to get in touch with busy people, check out the full post linked below.
How to Contact a Busy Person [Art of Manliness]