Witch hazel, as suggested works.
Try getting a mild corticosteroidal cream from the drugstore.
Monosodium glutamate, made into a paste, also works. This is sold in the stores as the meat tenderizer "Accent".
A slice of raw onion on the bite may help.
I've even used rubbing alcohol on bug bites before - but beware - if you have inadvertently scratched them or somehow broken the skin, it's going to BURN!!!
An over the counter anti itch cream may also help.
Do you know what kind of bugs they were? If they were chiggers, you're probably going to have to do more than just treat the itch - you'll have to actually get rid of the chiggers because they itch as they burrow into the skin.