The Virginia Department of Rail and Public Transportation recently released survey results from a travel study of both work and non-work trips. Unfortunately it grouped walking and biking together so we can't tease out details about just biking. While walking and biking are somewhat common in Northern Virginia, it's rare statewide. Only about 1.5% of Virginians walked or biked to work in 2015, the same number reported in 2007. But those who walk and bike to work are the most satisfied with their commute.
They're not as likely to be satisfied with the transportation system (42%), but they're still more satisfied than everyone except transit users. And they're the group mostly likely to support transportation funding - especially alternative transportation funding (but the difference is very small across groups).
Finally, young people are that much more likely to bike, but they're much more likely to walk.