I come from a chapter where COB was a way of life. The actual events worked, but sometimes, you need people to realize that your sisters are totally awesome. You know the people who never thought they would be greek until they met some phenomenal sorority women. (myself included!)
How we approached it was... we spent time with our sisters. We often invited other non-greek friends to hang out when we were hanging out. Then after people got to know each other and friendships were formed, it was easy to get them to an event, (whether it be for free food or games or studying or whatever.) And thus teach them more about your sorority.
Also, if your sisters LOVE your letters... sorority stuff just pops up, and those non-greeks may start to gain interest into what you do, or want to share in your fun times and stories. (Be careful not to be cliquey or over the top... just yourselves!)
On a campus where greek life is not the end all be all, it is important for the greeks to spend time with non greeks. If you end up 'converting them' GREAT
but if not, all you lost was NOTHING... and gained some positive PR (That woman might tell a friend considering it how nice and welcoming your chapter is, etc.)
I would just suggest going about it in an honest and open way.... calling it "undercover" or sneak a fied... makes it sounds like you are up to no good.