Have a look here and try doing what he does (I know the problem is different).
The key came from a comment buried down near the bottom of the page. Running fsck kept getting clobbered with a "Disk In Use" error, but this solved it:
FWIW, I found that even with -noautofsck, snow leopard would auto-fsck, meaning I would get ‘resource busy’ or whatever. I have no idea why it is ignoring my no-auto-fsck request. Whatever.
To allow the process to go, I ‘ps auxwww | grep fsck’ to find the PID, then ‘sudo kill (PID)’ to kill this fsck so I can run my own.
Killing the auto-fsck allowed me to run it myself. Not sure how long it took, I started it at 2am and it was done by the time I got up 6 hours later, but it was on a 500+ GB .sparsebundle, so I'm assuming it took a while.
Time Machine works at a file level, with no facility to perform incremental changes within files. As such, your Sparsebundle may be backed up in it's entirety every time it changes in the slightest, depending on how large it is. Of course, you have to wait up to 1 hour (+the time it take to make the backup, depending on how large the queue is and where your file sits in it) to ensure those changes are included in the backup. Also if your Sparsebundle is in use (mounted...) then it may well skip it until the file lock is freed
This is a terrible system, and one that we might not see change until the underlying filesystem is suitable upgraded (or replaced) to include such useful facilities as incremental block level changes rather than simple file level ones, and/or deduplication etc. One early victim of this scenario were users who used the original Filevault system for encrypting their home folders. Time Machine would not backup their home folders until such time as they logged out because the Sparseimage file was constantly locked by the fact the user had it mounted. And even when the user did log out, it would proceed to make a hugely inefficient backup of the whole thing again and again - on the assumption that they simply logged out and didn't just turn off etc... Not very clever. To try to ameliorate this the Sparseimage spec was ammended to allow for Sparsebundles. Instead of a single big file, a sparse bundle is a bundle (directory) containing a number of files called bands, each in the order of 8 MB in size. This means even though to the end user the sparse bundle appears as a single file, it is composed of smaller files. As of Mac OS X 10.8, the bands are 8.4 MB each. When the content of the image changes, one or more band files is changed, created, or deleted. This allows backup software (such as Time Machine) to operate more efficiently, but it's just a bodge to attempt to mimic block level changes in individual files, which is limited to 8Mb "blocks"...
So to answer your questions directly, 1) it handles them properly, where properly means the same as any other file, it's just that your particular use (leaving it open and mounted) may not result in efficient backups that are taken regularly, especially if you rarely unmount the file, and 2) yes, you will need to pull back the whole file to view it's contents. The TM restore interface is also file specific. It may have quick-look plugins to allow you to view simple files inline like JPGs etc, but not for a complex file like a sparsebundle.
On the bright side, you already have a licensed copy of ChronoSync, which is super useful, and I would continue to use this to perform incremental backups of your sparsebundle whilst it is mounted, you can use the same drive as your TM images too.
Best Answer
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’:
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.