Ethanol does not, per se, cause problems with K bikes. I've run tons and tons of it through all of the K bikes I've had and never had any fuel system problems. There is a BMW technical service bulletin (SB-00-021-07) which states that use of ethanol of up to 10% is fine in K bikes.
However, since ethanol tends to attract water, it has a rather limited shelf life compared to pure gasoline. It's not the ethanol that degrades the fuel system, it is the water that it attracts. This is why K bikes that sit for several years tend to have the vibration dampener reduced to goo, rusted and frozen fuel pumps or corroded gas tank leaks at the welds at the bottom seams of the tank.
Moral of the story: Ride your K bike often and don't worry about it.