Your landlord has a legal duty to provide you with pest-free, safe housing. Any effort your landlord would make to evict you after you informed him of the problem would be retaliation for which a judge might hold him liable. Give the landlord a call -- and make sure to follow up the call with a polite-but-firm note (keep a copy of the note for your records - you may need it!) If you believe that he WILL try to evict you, or if he gives you an eviction notice, contact the City's public health department so they can inspect and give the landlord an order to clean up.
Don't hesitate to contact a local landlord-tenant attorney with any questions you have.
No your Landlord Definitely can not kick you out if you ask him about the bedbugs. In fact, I'd recommend you ask him to remove them in writing. If he does subsequently terminate your tenancy, there's a prima facie showing that he did so in retaliation for your perfectly legitimate request.
As an aside, I personally am a Landlord and have dealt with bedbugs. If you do actually have them, you have to make sure to prep the apartment completely before the exterminator comes. Otherwise, you'll never get rid of them. This includes washing and drying all of your clothes and linens, and wrapping them in plastic bags.
You cannot be evicted for complaining about unsanitary conditions, that is called retaliation and is illegal. You would be entitled to sue if that were done.