Seeing an actual bug isn’t very likely, unless you wake at the crack of dawn. These insects are largely nocturnal, and tend to feast during the night. If you do find a bug in your bed, note that adult bed bugs are often reddish-brown, roughly the size of an apple seed, and relatively flat (unless they’ve recently gorged themselves on your blood). Nymphs (the young ones), on the other hand, are practically translucent unless they’ve just fed. In that case, they may look like bright red pinpricks of blood on your sheets.
You’ll have better luck looking for shed shells and exoskeletons, and dark brown or black stains (like an ink blot) on your bedding. Start by examining your mattress seams, the cracks and crevices around your bed frame (they love the little slots where IKEA bed slats sit), and even behind outlet covers.