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Given any closed, connected, orientable $3$--manifold and integers $g\geqg(M), D > 0$, we show the existence of knots in $M$ whose genus $g$ bridgenumber is greater than $D$. These knots lie in a page of an open bookdecomposition of $M$, and the proof proceeds by examining the action of the mapinduced by the monodromy on the arc and curve complex of a page. A corollary isthat there are Berge knots of arbitrarily large genus one bridge number.

Bridge numbers of knots in the page of an open book