I'd have a problem even with that, unless -- and I think this is the issue here -- the food and water are also available without Bible.
I agree in general, although simply handing someone something in the general vein of ``I think you might get something out of this'' without any other pressure is fairly innocuous. I think it's along the same lines as the Gideon organization that, at least in the US, puts Bibles in many hotel rooms for free. (Of course, I'd hate to think the outcry that would occur if some organization were to start also placing Qu'rans or Bhagavad Gitas or Torahs or whatever else you might have.)
I don't think that saying ``feel free to take one'' is wrong. It just provides the possibility for increasing knowledge, and despite my religious misgivings, understanding someone else's beliefs has the strong possibility of helping one empathize with them more.
On the other hand, I understand where you're coming from, that a Bible forced into someone's hands is offputting and makes it feel like a requirement, although I have no problem throwing away Chick tracts at the next trash can.