|This really depends on time of year and local climate. In the UK, I usually figured 24 hours to dry, but in the spring and fall when it was very damp but before the heat was on, that was sometimes longer.
I'm now living in CO, and everything dries super fast. I still usually leave the diapers for a day, just because, but they are usually dry in far less. Both of those times are indoors; outdoors is usually lots faster.
Personally, I think it's well worth buying a few extra diapers to have the time to line dry. You save a lot of money in drying costs and I have to believe the environmental impact is less. It's also obviously better for the diapers' longevity, too. Hurrah for drying racks! :-)