I have a double too. I'd guess that I'm in the big ring about half of the time. It really depends on the terrain. I tend to use my cadence to dictate what gear I'm in. For flats/rollers, I aim for 90-95. I can usually do that in the big ring. For climbs, I'm usually in the small ring maintaining a cadence in the 70s. Well, unless the climb is long & steep and I run out of gears. Then, I go with the cadence that allows me to maintain forward momentum
I always shift into the big ring as I come into a downhill. That way you can carry the speed of your descent into whatever comes up next.
2004 Colnago Chic - WTB Deva
2008 Blue RC7 - WTB Deva
2009 Colnago Master X-lite - WTB Deva