do not do it this way

Have her BG/Fiance file for a K-1 visa (Fiance(e) visa) for her in the US. This way she can enter US and get married in US, and wait for GC in US. This is the fastest and easiest way.

If they have to get married in Canada, she'll have to be separated with him for a while (several weeks at least) until he files petition for her GC and when GC's approve.

She will not be able to get any non-immegrant visa since her hu*****and is in US and is US citizen.

See below sites from USCIS for details:
http://uscis.gov/graphics/howdoi/spouselive.htm
http://uscis.gov/graphics/howdoi/Appproc.htm

See below sites from DOS about how to get a Fiance(e) visa K-1:
http://travel.state.gov/visa/immigrants/types/types_1315.html#4a