Bed bugs are not "ordinary wear-and-tear." The tenant is responsible for any damage that occurs at the apartment beyond ordinary wear-and-tear, unless it was somehow caused by the landlord.
Sometimes landlord include extermination as regular part of their maintenance of their buildings, but they're not likely to if there's no history of problems.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.