While I would certainly agree that a woman must have her face available for a ID card such as driver's license or OHIP, and must show her face to have her identify confirmed when asked by police etc, I don't think that allowing a burka is any more offensive than head coverings by Orthodox Jews or the Sikh kirpan.
And if a woman is religious enough to wear a burka, I don't think that she will be "liberated" enough to enter into business contracts. And if she does seek to enter into a business contract, then I would suppose that her religious beliefs could be bent enough to allow you to confirm her identity.
As for being pulled over for having a bandana on your face, I guess that riding a motorcycle might have something to do with it. I've never had any problems with full face protection while riding a sled.