You must realize, we are in the 240th century. the year is around 23,000. What use would a bow be? A survival tool, surely, but we have disposable clones. Long term survival means nothing to us. And a bow isn't something you can just pick up and use proficiently. It takes years of practice and training to hit targets beyond 30m with any degree of reliability, whereas guns can be deadly at hundreds of meters in a few weeks.

So a bow is only as useful to us as immortal mercenaries in how immediately deadly it is. Remember, we aren't dealing with olden armors. we have tritanium armor layers with energy shields. A bow would have to be immensely strong to get through all this with any degree of reliability. So a bow would be very unlikely to be implemented.

Now silencers and guns made for stealth, these would easily exist in the Eve universe, especially amongst the Minmatar. But as for a bow and arrow, the technology is millennia out of date for the level of technology we use.