The one carb'd bike we have left here, a 2003 Triumph Trophy, is extremely quick to come off choke- no more than 10 seconds. Everything else is fuel injected. By the time I put my helmet and gloves on, they're ready to go.
2005 Suzuki V-Strom 1000 (for sale)
2003 Triumph Trophy 1200
2009 BMW F650GS (wife's)
2012 Triumph Tiger 800