My only experience of running WinBUGS from within Stata is under Windows and Linux, but Tom Palmer, who was one of the authors of the original Stata Journal article on this topic http://www.stata-journal.com/sjpdf.html?articlenum=st0115, recently sent me instructions on how it can be done on a Mac. If you think that those instructions might be helpful to you then you can download them from here, winbugsfromstata_on_mac.
If you have any queries about the instructions, then you should contact Tom directly at t.m.palmer@warwick.ac.uk .
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Thanks for sharing those instructions. I successfully installed OpenBUGS on a Mac.