What kind of bug bite is one where there is a bruise around it?
Answer: It could be pretty much any bug. Bruises are caused by bleeding under the skin, which can happen with any type of bite. Typically ant bites do not bruise; mosquito bites sometimes do; and with a spider bit it would depend on the type of spider.
A description of the bite would be helpful. Is it a raised, red, itchy bump? Mosquito. Is it a raised red bump with a white pustule? Ant. Are there visible puncture marks? Spider.