If I change the Product of multiple bugs, I get to a screen that requires me to
change both the Version and the Component. Ideally, it should ask for the
Version and then, in a separate screen, ask for a Component name in case the
original Components don't have matches in the new Product/Version.
Components in Bugzilla are currently tied to the Product, not the version. The
Versions are also tied to the Product. So currently your suggestion is not
needed since all components are global to all versions anyway. There is a bug
submitted at bugzilla.mozilla.org for an RFE to make this happen. But probably
will not since it is not a trivial change.