Bed bugs are among those insects that are given structures like beaks that can pierce into victim's skin. Such insects use those structures to suck and sip blood from victims.
Insects normally are not carnivorous. So are bed bugs. But you may have a different classification for them because of their eating habit. Somehow, they can be related to vampires. Don't be amazed. Of course, that is just to tickle you with a little sense of humor.
Because bed bugs, and similar insects, prey on and eat blood, it follows that their excretion is also having resemblance to blood. As they say, what goes in is also what goes out.
Hence, you can find that bed bugs' craps and pee are red or deep-red colored. They may appear as such tiny red stains in your bed, your bed sheet, furniture surfaces or wherever they may have contact with.