How long does it take to get confirmation?
It depends. It can take a few hours for a personal enrollment to several days for a company enrollment. If you want your company name (rather than your personal name) to show up on your apps, you'll need to take the extra time to confirm.

I also suspect that during times of peak enrollment (say after an announcement like at WWDC) that the confirmation takes longer simply due to the number of people applying to play with the beta.