As soon as you enter your hotel room and put down your luggage (use the luggage rack, not the bed), check the mattress for bed bugs.
Here's how: Remove the pillows and strip back the sheeting so that you can inspect the seams of the mattress all the way around. Bed bug droppings look like spilled pepper, and there may be dead bugs and further evidence under the mattress. Should you see these tell-tale signs, immediately return to the front desk. You can ask for a different room. But if it were me, I'd check out and switch to another hotel.
P.S. One way that bed bugs find their way inside is via luggage. Dragged along the street, suitcases can pick up bugs from discarded, infested furniture. To make sure you don't transport bed bugs into your own bed, check suitcase seams before bringing luggage inside and don't unpack on your bed.