Bed-bug-free room? Fantastic! Unfortunately, the risk is not completely gone. For one thing, you (and the hotel staff) may have missed a subtle sign of infestation; and for another, bed bugs can travel through the walls from room to room.
So, maintain a few protective measures throughout your stay. Keep your bags off the beds and upholstered furniture; instead, leave them on tile, a shelf, or the (previously inspected) luggage rack. Don't toss your clothing on the floor after you wear it, and any clothing you wear while in the room should go into a plastic bag when you're done with it.
Basically, be just a tiny bit paranoid. You're probably in the clear, but absolute certainty is tough when it comes to bed bugs.
And finally, for the most serious of bed-bug preventers ...