Bed bugs do not live in the mattress. They come out at night from crevices or cracks in the wall or baseboard and bite. Since it is a townhouse, both sides would need to be done at once. If you "bomb" one side it will just move them to the other and then back to yours. Same with cockroaches.

In some cases, a good, hard cleaning can do the trick. When we moved into my old house we had bed bugs. We went through and basically bleached everything and never had a problem since. It's hard to tell how bad the infestation is since you don't see them during the day. And wrapping plastic around the bed will not do anything either.

I would talk to the neighbors about having an exterminator come to both sides and definitely tell the landlord because this should be taken care of NOW. But on the bright side, these do not carry any diseases and are just annoying. But they can indicate other unhealthy circumstances.