We have a suction tool, I think it's literally called the bug bite thing or something. Basically it suctions on to your arm where the bite was and you pull your skin up into this tube and it sucks out the venom that causes the itching as well as the stinger if one was left behind.
My wife and I haven't had a bug bite any time we've had that thing handy, so mainly we just put it on each other's nipples for shits & gigs. I can't really say that it's effective, but it is fun.
This, but I use the hottest water I can stand under the tap and go a few times.
The way this works is because the reason a mosquito bite is itchy is due to an enzyme in mosquito saliva which locally numbs an area when a mosquito bites you. Once the mosquito saliva enzyme starts wearing off, it registers as itchiness until the enzyme is completely gone. So, using heat to denature the enzyme, making it impossible to do it’s job, makes the itching go away.
I thought the itchiness was due to your immune system reacting to the saliva. And as you scratch it, you cause additional inflammation which causes a bigger response and thus more itchiness.
Whatever it is, killing it with fire works. Though I got a bit carried away a few nights ago and I have a burn mark on my leg now. Be careful kids!