My time machine has three sparsebundles. Obviously something wen wrong long time ago.
I am also missing files for a while and most probably they are in the oldest sparsebundle.
How do I access a specific sparsebundle and explore files in them?
Might be easier to do it manually than try to persuade the Time Machine GUI to use a specific one (if that's even possible). Double-click the sparsebundle and it'll mount like any other disk image. You'll find the individually-dated backups under the /Backups.backupdb/(computer-name) folder.
If you press the option key when selecting the Time Machine menubar icon, it should allow you to select a different backup disk (a different sparse bundle) to browse.