Time Machine — ‘Sparsebundle already in use’ error
After some research, I found the answer was pretty straightforward, though not obvious. As the error message hints, the problem is that the disk mount utility believes that there is already a user connected to the disk. To solve that, you can use a handy function present in Airport Utility 5.6 (but not in Airport Utility 6.1), named ‘disconnect all users’: 


Open the Time Capsule pane by double-clicking on the Time Capsule item in the left list. 
Select the ‘Disks’ tab. 
Press the button ‘Disconnect all users…’ 


If you don't have the Airport Utility 5.6, you can either download it from Apple's KB (if you're on Mountain Lion you'll also need the Pacifist app to extract the app from the package) or just use your Airport Utility 6.1 to reboot the device.