Why are there no bows in fallout?
Why are there no bikes?
There aren't bows in fallout because they aren't common weapons in this century, only a small handful of people know how to make a bow.
Ok... just about every pawn shop and sporting goods store on this continent has a compound bow for sale; The sporting good shop would have self bows and more complex hunting bows as well. And Fallout (the setting; not the previous games themselves), would have a had 50's-esque bow sets for teenagers, and young advlts. Lil' Bear youth scout bows for the kids, and full size bows for Dad ~and Mom too.
I'm still surprised that Fallout:New Vegas (and FO3) didn't have one, because there could have been an entire stealth aspect for using silent range weapons, and there is the fact that the engine supports pinning limbs to the wall; and Oblivion at least, had arrows embed into enemies and the PC alike.
In Fallout 2, people were making rifles out of pipes and rigged parts for need of a gun; and lacking that even used knives and spears. People
could (and would) make bows.
The excessive prevalence (in FO3) of firearms, high tech, and even nuclear weapons was a real disappointment for me. In Fallout you usually only found such in an isolated and dangerous (perhaps even rarely discovered) locations ~or you might find some in the larger settlements where others had acquired them, and they weren't cheap.