no, dust mites are tiny microscopic creatures, their jaws would not be strong enough to bite a human (they eat tiny microscopic pieces of dead skin cells etc) However if you are getting bitten while in bed you might want to check for bed bugs (you can see them) just pull back your bedding and look at the mattress.
Dust mites are too small to bite people. If you are getting a lot of itchy red bites at night it is more likely to be mosquitoes, bed bugs, or fleas (if you have animals). All of those can be really itchy. I've heard (but don't have first hand experience) that bed bug bites tend to occur in groups of at least 3.