Somebody been watching Arrow on TV? :)
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Have you looked at the rules for Improvised Weapons? It's basically a GM's call to make based on the size and build of the weapon. At my table, I only give a medium-sized longbow 1d3 damage if you're using it to smack people. For me, it's about the contact area, shape and weight of the improvised weapon. Longbows tend to be pretty thin and flexible so I figure bludgeoning someone with one shouldn't elicit more than a sting comparable to being struck my a ruler.
Still, that's me. Another GM might rule differently.
If the bow is already strung (i.e. ready to fire arrows) then I personally wouldn't allow it. Or more accurately, I would allow it only once and it would break the bow. They're under a lot of strain and not built to handle excess strain.
Once I tried stringing a longbow that was fairly old (I found it in a basement of a home we bought, not sure how old it really was). It snapped and half of it flew straight up. I ran for shelter, not knowing where that would come down. It took a few seconds for it to return to earth and it speared into the ground about 5 feet away from where I was standing when it broke.
Long story short, bows are like tightly-wound springs under a lot of stress when they're strung. Smacking someone with one would certainly be bad for the bow. Nobody makes them extra thick or extra durable - doing so would make them harder to draw and fire (by Pathfinder rules, that means making them compound with a higher STR modifier - but since everyone always tries to use bows that are perfect for their STR, nobody would use one that is "extra" anything or it would be too hard for him to use).
Now, if it's unstrung, it's basically just a straight stick like a slender staff and should be perfectly fine for improvised bashing at, say, 1d4.