The bugs wouldn't have arrived in a brand new mattress but even if they had, I doubt that they could have survived two years without feeding. It's far more likely that the new tenants brought them and that they traveled through cracks in the walls and from room to room through the (hollow) walls themselves.

I wouldn't bother with the bug bomb, especially not in just one room. Even the bugs in that room are going to be hiding in cracks, folds and seams most of the time and the insecticide fumes may not get to them. The bugs in other rooms -- or inside the walls -- won't be affected at all. Everyone I know has had the best results by patching (or eliminating) the cracks where the bugs hide, then going after the remaining bugs with something like pyrethrins. Once a mattress or other stuffed item becomes infested it may be necessary to get it professionally fumigated or hauled away. Bag such items tightly in plastic before moving them, and be careful not to let someone "salvage" them and spread the problem farther.

Here's the Wikipedia article on the little beasts. For a little more on bedbugs (my experiences and others'), see this thread.

Good luck, r_f!