The Bible, as an inanimate object, cannot be considered either patriarchal or matriarchal.
The cultural ways of life recorded in the Bible, however, are definitely patriarchal in their orientation and functions. The primary role of leadership, responsibility, and ultimate authority in the ancient tribes of the Israelites and the structure of organization in the nations and tribes in the Middle East was given to male leaders most of the time. The lineage of the Israelites was based on a very patriarchal system - Abraham, Jacob, and Joseph, whose twelve sons gave their names to the twelve tribes. There are a few exceptions in the Old Testament, such as Deborah in Judges chapters 4-5 and the recognition given to Queen Esther, but the stories of women in positions of authority are rare.
Jesus's recognition of women was highly unusual, if not scandolous, because it was expected that women would be kept separate from contact with males outside their immediate families. As groups of Christians began to come together after Jesus's death and resurrection, most leaders of the early churches continued to be male.