Mini Cooper 2004 40,000 miles, 1.6 liter

I can hear a noise that sounds like my wheel bearings coming from the back of the car. The faster I drive is the higher the pitch of the sound. I had the rear wheel brakes done today. With no change in the sound. Granted, the brakes were in a terrible state according to the mechanic.
I am concerned that the dealer contends that thie bearing are not covered by the warranty. BTW the car is 3 years into its warranty which means it has one more year to go.
Are the bearings covered. Is there a recall on my year and make for just such a problem. I have seen many instances of problems identical to mine on the same model. I would appreciate a prompt reply. I am at my wits end as to what to do.
I have been told that the only method of determining the problem is do do exploratory surgery. I.E. For a prce the mechainc will open the housing and check to see what is exactly the problem. I would hate to pay for this and then find out that the bearings are not exactly the problem.