I can't find anything specific regarding this but I would say no. A bow in itself is not a two handed weapon per se. Yes I know that one hand holds the bow whilst the other loads and pulls the string. The difference really is the fact that the bow is a ranged weapon. 2H weapon style grants a bonus because a shield isn't used in melee combat as I understand it. Seeing as the bow is ranged and not wielded as say a sword is I think the answer is no. Basically to my mind, any Tom, Dick or Harry could pull a bow string and point it in the general direction of an enemy from distance whereas a 2H sword means getting up close and personal to an enemy with little personal defense save your proficiency in the weapon. I could well be wrong but that's my take on it. You could check for yourself of course by having the "to hit" rolls displayed and see if a critical occurs with a bow on a roll of 19.
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One love, peace.
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