If I bought ne furniture when I moved into my apartment 3 months ago and now I'm told there are bed bugs, who is responsible and what are my rights?
Possibly no one is responsible: the landlord *might* be responsible if you can show that they do not exterminate regularly or at reasonable intervals, and/or that they ignored (have not responded) to a known bedbug outbreak in the building of which they are provably aware. But if the landlord does take reasonable (not perfect--just reasonable) steps to avoid or deal with pest infestations, they are not responsible for those infestations that do happen--sometimes even clean tenants and clean buildings get pests (e.g. bedbugs) without it being anyone's fault and the law accepts that. You'd have to show landlord fault in some way to hold the building liable for your bedbugs (e.g. the cost to clean or replace furniture). This is in regards to holding them liable for any costs or losses you have incurred.
You are, however, on a forward-looking basis entitled to have the landlord deal with the current problem within a reasonable amount of time after you notify them of it. If they do not take steps to deal with the current infestation--and again, within a "reasonable" time frame, which could be days or even a week, week-and-half if they try to get an exterminator but the exterminator is booked up--then you may be entitled to withhold rent until the problem is addressed.