That is tough. At 3, I am sorry you're experiencing this... The things that I would suggest... when she starts thinking she has a bug on her, take her to a mirror and show her the place she thinks the bugs is. If necessary, allow her to remove items that are blocking the place where 'the bug' is. Even further, if she continues insisting, offer a chance to take a bath or shower. This will redirect her thoughts and make her smell all pretty :)
It will take a while for her to realize that the bugs are not there, but as you show her, she will start seeing that there is nothing there.
Another think I would try, start introducing her to harmless bugs, like lady bugs or rolly polly's... I wouldn't suggest she holds them, but maybe if you do, she'll start seeing that it is ok for some bugs to be around.
The most important thing though, is don't get upset yourself. If is hard to keep your calmness, but it is necessary for her that you stay calm no matter how frustrated or scared you get. Luckily, all kids have phases of fears, and hopefully she'll come right out of it.
Hope it helps!