Why do you want to pursue your research interests within the framework of OB (rather than in some other framework)? Business schools often take applicants from a variety of backgrounds and a quantitative background (especially if it involves coursework in statistics and experience working with data) is often useful. However, you really need to articulate why you want to pursue a PhD in OB and connect your research interests and past experiences to the school's focus. Has your past education/work caused you to become curious about a particular research question that is best addressed at Stanford (/whatever other schools') OB Dept? Have you read the OB literature, and after reading it realized that it interests you more than other fields? You really need to address such questions in a convincing manner.
Also since you mentioned Stanford, have you considered this program? STVP : Research : Doctoral Studies To me, this looks like a more natural fit for you than an OB Dept, but of course you know your interests best.
I wouldn't get a recommendation from someone you only sort of know. If you think you have time to get to know the professor better, you can contact him/her and express your interests and see if you can meet to discuss research of help him/her with some RA work. However, I'm not sure if you have enough time for that at this point.