In a single family house rented for more than 10 years, in Los Angeles, is the landlord responsible for removal of bedbugs?

That depends on what the lease/contract says about extermination policy. Read your lease/contract. Or are you the landlord?

Bedbugs have to be brought in. They do not live out of doors. If the property has been rented to the same tenant for the entire ten years, the tenant needs to figure out where they came from so the bugs don't keep coming back.