Slowly remove the sheets and look on both sides of the sheets for small black marks or small red marks. Check the mattress surface for the same marks. Small black dots indicate feces from bed bugs while small red marks are blood indicating bugs were feeding recently.
Look closely at the surface of the mattress and box spring. If there is a bed bug infestation you may a gathering of bed bugs. Look out for small brown flakes which indicates skin that bed bugs have shedded.
Run your fingers along the seams of the mattress and box spring. Lift up the mattress and run your hand along the space between the mattress and box spring. If you feel anything moving you may have live bed bugs in your mattress.
Remove the headboard if possible and inspect the bottom and back of the headboard for either live bugs or bug feces.
Place double sided tape around the bed post legs and along the perimeter of the box spring and leave it overnight. Inspect the tape in the morning, if there are bugs trapped on it than there is an infestation.