I even applied before getting the first AOR since my WP was expiring on Apr 13.
There are a couple of threads on the Canadian Experience forum that explain how to fill in the BOWP application and how to handle without getting AOR.
http://www.canadavisa.com/canada-immigration-discussion-board/-t139027.0.html
http://www.canadavisa.com/canada-immigration-discussion-board/got-my-bowp-approved-without-submitting-aor-t153061.0.html
Basically I first followed the wizard on CIC and select temporary option. Than you get to the work permit part, where you can do the online application, which I did.
The threads helped me to fill in the application forms, since the same forms are used for closed/open work permits.
Now I'm waiting to see if it will be approved. Based on the current timelines I think it should be processed somewhere next week. Yesterday I got updates for it, but nothing visible, so I guess I'm getting closer to the processing.
I'm rather nervous for it, since the rules were changed and it is no longer sure it will be approved with the first AOR. So I can only hope and also hope the PR might be getting there as well.