What you want to do is look for the bugs or their 'droppings' (small black stains) in the folds and creases of the mattress. If you see these, you can do one of two things.
Steam clean everything. With a serious steam cleaner. We use a Shark, because its the only one on the market that gets hot enough to kill the eggs. You need a steamer that gets above 140 degrees. Steam clean the whole room. Cover all outlet plugs, as they can migrate through there. Then you will want to go out and buy (or order online) a product called Diatomaceous earth. You can get a food grade version, and its safe enough to eat, though I don't know why you would try. Treat the mattress. Treat the carpet. Treat everything. Put all of your pillows in the dryer, and dry them as high heat for 30 minutes.
Option 2 - buy new everything. Easier, but more expensive. If you did this you would still want to treat with Diatomaceous earth.
Bed bugs can lay dormant for over 9 months. They suck. Literally.