Can I use my keys to enter a tenants apartment so that I can have it professionally sprayed for bedbugs, even though the tenant refuses me entry?

Generally speaking, Landlords must give tenants “reasonable notice” before they enter to make non-emergency repairs, or to show or inspect the apartment. “Reasonable notice” is normally 24 hours. Entrance can also only be at “reasonable times.” “Reasonable times” are usually during the day or evening, not in the middle of the night. In an emergency situation, you can enter the home with shorter notice or without notice.  The tenant can not refuse entry.  Give the proper notice under the law and I would do it in writing - and you should be fine.  Good luck.