I work for a property management company in New York City and I will take a stab at this. I have worked with several co-ops where shareholders have in fact been charged for the cost of exterminating bedbugs. In every case I've encountered, the complaint was answered quickly with an exterminating visit arranged and coordinated by the management office. All neighboring apartments are treated at the same time as the one which called in to prevent further infestations.

Regarding the cost of bedbug extermination, affected shareholders have called my office and insisted the co-op handle the cost plenty of times. In one case, I was told by a shareholder that she would call 311 if it was not resolved, and absolutely refused to allow exterminators to enter unless the managing agent or Board of Directors promised it would be free for her. The board refused, and in the process of debating the issue, lost a few valuable days when the bedbugs could have been spread. Finally, the board gave in and shouldered the cost, although in an attempt to look strong, said it was only under the pretense that her neighbor had a prior infestation and was living in a severe hoarding situation where it likely started. A unified board would have demanded access, and by giving in here, I feel it opens itself up to future disputes on an issue that should be resolved without argument.

Please be mindful that this new management company likely does not want to manage from a place of weakness - bedbugs must be dealt with, not negotiated, and shareholders with ongoing infestations will be more inclined to clean up and toss away potentially infested furniture, etc. if they are charged for exterminating visits. Shareholders generally will decide on an exterminator based on price, and many if left to their own devices will shop around for a less-than-adequate service in my experience.

I have met exterminators privately who tell me the largest issue is the preparation work required by the resident - laundry, furniture, beds, and all types of materials need to be tossed/cleaned/treated or their chemical/steam treatments will be all for naught. A side industry now exists for "bedbug prep companies" because many apartments require serious preparation removal of furniture/upholstery, etc. for a successful bedbug treatment. A compromise some coops engage in is that the coop will pay for the exterminator if the shareholder pays for the bedbug prep company.

Although it is true that you did not bring the bedbugs in, the co-op legally can bill you back for the exterminating service.