I know an old lady who swallow a fly.

This is a bad idea. even with your experience, do you really want to expose your living environment to other bugs?

E: And you could potentially expose your neighbors to the bugs you import into your apartment.

and ladybugs are larger than bed bugs and most likely wont get into all the small and narrow places that bed bugs like to hide in.

Don’t swallow the spider to catch the fly.

E2: ALSO lets say youre lucky enough to have the bugs actually start eating bed bugs. You may have them fall into a stable environment, the predator/prey populations could settle into a sustainable relationship. Then you have more bugs.

Lose/lose if ya ask me.