What is the biggest threat range I can get on a bow? Obviously I'm aware that improved critical doesn't stack with similar effects, but are there other ways to increase a bow's threat range instead?
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Assuming you are taking about critical hit range of a bow and not threaten squares.
The only ways I know to increase the critical hit range is via the improved critical feat, keen weapon ablility and the keen edge spell. Multiple effects that increase a weapon's critical threat range don't stack.
There is a way to effectively increase a weapon's critical threat range by using Perfect strike feat (see Zen Archer Monk) or some other multi roll effect. Rolling two or three d20 and deciding which to use doubles or triples your chance of getting a critical threat number on the tohit dice.