I'm not quite sure why it occurs, just an physiological resopnse to anxiety.
Theres probably no drug for it, but the reason you may feel like its a problem because of what you think others will think of you.
Try not to think of it as much and concentrate on something else, create a distratction in your mind. Relax!
Your not a mind reader, you can't honestly tell me that you know what people are thinking and especially not of yourself. The more you think about think about it the attention you bring to yourself.
What would you tell someone in your situation? you wouldn't tell "them bloody hell your blushing, you look like a right idiot", its just not done if they are a decent person,so is there a need to think that way about yourself.
Forget the blushing sure you a great person and if they can't see passed that fuck'em!