Fred Bear was right-handed and, as far as I know, his dominant eye was also the right one.
Nevertheless he shot left-handed - why?
Having done a bit of googling it appears he appears he shot left-handed due to an accident where he had part of one of his fingers amputated:
...Fred Bear shot the bow left handed, but he was right eye dominant. He had a partial amputation of one of the fingers on his right hand, so it was either draw left handed or only draw with two fingers of his right hand. Everything else he did right handed, including shotgun shooting.
this also appears to explain why in earlier photos he shoots right-handed. He switched after losing his finger (I'm reading between the lines here a little)