Airbox on mine was far bigger jumps, up to 3,300 RPM and off idle. It would lurch back and forth pretty bad while riding and often I had to pull the clutch in for gridlock traffic. Near the end, it would flat die with the clutch pulled in. They first did the solenoid motor for the idle (BMW approved cheaper fix first), and later airbox 2 or 3 which stopped the really radical idle swings. Probably just gets all sooty for minor 200 RPM swings.
However, mine now idles much the same as yours, 900-1100 RPM. I don't worry about that as it is not as bad as hanging up at 3,300 RPM off throttle, or just outright dying by pulling in the clutch which is worse.
It may be the gas too. I put some $13 gallon stuff into it once and the thing ran like a top and never wavered on idle. The good stuff here comes in blue or orange cans in the USA and commonly referred to as off-road, marine, or race fuel. I don't know if this cheap corn-oil gas is all that hot. I know the BTU numbers are down using it as well as the mileage number per gallon. I don't think they designed the bike to run with this corn oil in the USA as they added 4 more injectors on the S1000RR over the K1200/K1300 engines (the S100RR has 8 injectors).
Fwiw, I know some Harley guys are using the $13 per gallon fuel in their CVO 110 inch H-D engines as they claim they idle better and less soot in the injector bodies. Guess if you got the $42,000 for a CVO version, then paying $13/gallon for fuel isn't bad to make it idle decent. Some mix it half and half. Dunno.
I mixed in some Harley fuel stabilizer ($6 a bottle) into my two bikes yesterday since I haven't ridden them in over a month since this busted hand crap and I can't pull in a clutch lever. The H-D shop guy said this fuel isn't lasting well in storage in a month and to run the bike a bit and to add it so I did. Only added about an ounce to each bike as I was told.