Is there any way to transform a PC into a swarm of bats without breaking any of the official rules?
There are no features that allow you to transform into multiple creatures at the same time.
Wild Shape and polymorph are explored in these Q&A:
- Can a Druid Wild Shape into a Swarm or "Giant"?
- Can you take the form of a swarm with the polymorph spell?
The issue is that every feature that allows changing form changes you into a single creature, and a swarm is not a single creature. It is treated as a single creature for the purposes of combat mechanics, but it is still a plurality of creatures. This is the obstruction to using Wild Shape and polymorph, and it holds for every other feature that allows you to transform. A single creature cannot become more than a single creature.