Wow, that's a lot of bug bites! My sympathies. Not sure about all bugs, but mosquito bites itch because the saliva (which is an anti-coagulant that prevents the blood from clotting while the mosquito drinks it) causes an allergic reaction, which in turn causes swelling and - you guessed it - itching.
Our bodies usually get used to the saliva, and the allergic reaction no longer occurs (that's why kids are often more sensitive than adults to bites). The exception would be if you're very sensitive to the saliva.
Hope this helps! :)