It's certainly possible there are multiple laws that would apply in such a case. However, I can say that you should definitely be licensed before accepting any monetary compensation from your friend to "watch over" their bedbugs, either at your place or theirs.
Also, if your friend compensates you to get rid of the bedbugs that "followed" you into your home, beware that this money is not considered "remuneration for unlicensed bedbug-sitting".
Of course, just to be safe, you may still choose to acquire the appropriate licenses, permits, and pass the appropriate animal-care and handling courses.