Set Billing Address to be Not Required in Contribution Page
I am surprised that Authorize.net does not require a billing address!  I don't recall ever seeing that.

With that said, I would recommend you still require billing addresses.  Right now the volume of fraudulent credit card transactions on non-profit sites seems to be skyrocketing and anything you can do to protect yourself would be prudent. The last thing you want is to have Authorize turn off your account due to fraud and you won't get any contributions then!