I don't understand, why you would call it a bite, when a mosquito "bites" you.
I'm fine with saying "bite" to a wound produced by a tick or other insects that actually have a mouth or something comparable.
But mosquitos, they don't have a mouth or teeth with which they could bite you. In my opinion, they sting you.
This is even worse for wasps. They really sting you with their sting to defend themselves (and not to feast on your blood), yet still some people call it an insect bite.