yep its every 6000miles (10 k kms) for the tiger. The 4k does not apply to your bike. Check the service schedule. i think provided the dealer knows you going over is unlikely to be a problem. it seems in the UK it is damned near impossible to book in for a service much less than a month in advance so you cannot say for certain your bike is going to be under or on the specified interval. I guess as has been said +10% would be reasonable much more than that and you could be pushing your luck if something happens before the bike is serviced.
we are fortunate over here that we can normally get the bike serviced "within" a week of the request