Not sure about the area you live in but, I would check out the landlords legal obligations and yours. If the bedbugs are confined to just your unit a speedy treatment might do it and they could have come in with you at some point. If they are everywhere they would have a hard time claiming it is your fault.
Hotel rooms and luggage seem to be a common vector for transporting these pests. They are showing up even in the best 5 star hotels.
The only people I know that have had to deal with these bugs have not had any reptiles so I am unable to help on that front.