I think the word “monk” is understood differently in the eastern and western Churches. In the western tradition, a monk is generally considered to be a member of a monastic religious order, who may not necessarily be a priest. In the eastern tradition, any celibate priest is considered a monk.
By the western definition, probably very few Orthodox bishops are “monks”, as most would probably be selected from what would be considered in the West to be diocesan priests. (but I admit I have no real data about whether any Orthodox bishops are actually members of religious orders.)
By the eastern definition, all Catholic bishops are “monks”, as all are celibate.
