For this reason I was wondering if the patch-bundle route would be a
clean way to push stuff to bzr.
No. Why do you think it would be any better than anything else? Once
you've got atomic commits, the rest of the issues are "what metadata
does your VCS record?" which are pretty similar for the VCSes under
consideration, and genuine conflicts, which have to be resolved
somewhere. VCSes aren't magic; when you and I make different changes
to the same line of code, some human has to sort that out.
The problem with bidirectional mirrors is that humans are "supposed"
to be out of the loop at the point where genuine conflict occurs.
Unidirectional mirrors don't face this problem, and with a local bidi
mirror, responsibility for the problem is clear and equal to the
person who will experience damage/inconvenience.