There is no harassment for a landlord to enter your apartment to conduct an inspection, in your absence, for the presence of a pest infestation. The LL has an obligation to you, and the other tenants, to react swiftly to potential infestations and disease vectors (i.e. bedbugs, or rats/roaches/mice/etc)
As for the Inn or the hospital, it's unclear what you're referring to, and likely is irrelevant to the question. Ultimately, if you're not responsible for the bedbug infestation, you probably cannot be charged for the extermination. Nor is it possible (legally) for your LL to increase the rent on your unit (or the other 343 units) to cover those expenses in the midst of a lease term. However, a reasonable rent increase may be assessed to new tenancies or lease renewals with sufficient notice.
The foregoing is not legal advice, and nothing in the foregoing shall be deemed to create an attorney client relationship. If you feel you need to speak with an attorney regarding your issue, it is recommended that you contact an attorney with expertise in your area of inquiry. The information related above is purely for informational purposes, and should not be acted upon without speaking with qualified counsel familiar with you specific situation and the laws related thereto.
In New Jersey it is the LL responsibility and cost to remedy bed bugs. It is also contrary to Section 8 regulations to charge for pest control as additional rent. However, pursuant to Section 8 regulations you are required to maintain your apartment in habitable condition. The LL and Section 8 may inspect your apt to determine whether you are maintaining your apartment. I suspect you may have some housekeeping issues. Maybe you need social services to help with housekeeping services.