In terms of physical skills they are equally matched. Mary is at a disadvantage because her Bloody persona doesn't attack women. Barring that however, I just don't think Betsy could deal with being set on fire and showered with a hail of gunfire and shrapnel. Bloody Mary's kind of an overwhelming force.
Betsy doesn't wear much and seems to be more of a close quarters fighter. Mary can ignite anything in her line of sight and as Bloody Mary, uses firearms, shields herself with improvised armor, and tends to surround herself in a deadly cloud of shrapnel. Both are equally matched physically, maybe Mary has an advantage because she uses her powers to greatly increase her agility and dexterity and has been shown to be capable of catching and redirecting bullets with her Ninjoto swords. I think in a situation where she was convinced Psylocke was male, Mary would win simply due to the distance issue.