In order for a mosquito to make contact with skin under clothing, the fabric must be skintight or close fitting, such as yoga pants, lightweight undershirts, or tights.
If you’re wearing loose clothing made from an impenetrable fabric, mosquitoes won’t be able to bite you unless they’re able to get into the garment.
So no, mosquitoes do not bite in the regular sense of the word, but neither does it sting. So 'bite' is used for convenience. It is only the female that bites, because it is only the female mosquito that needs your protein for its eggs! And mosquitoes suck!