Okay, I don't know if this bug has been fixed or not, but as far as I know, followers do not like bows that you give them, however I have just completed the companions questline and gave Aela my nord hero bow in vain hope that she would use it. She did. but then, I noticed her picking up bows of of corpses and using them! I checked her inventory and sure enough, there was a hunting bow, an imperial bow, the nord hero bow, and a forsworn bow, has anyone else had this happen? In a previous game she wouldn't equip any bow I gave her but now she does.
Dieter, I went to trade with her after a battle at a forsworn camp and she had 4 of their bows in her inventory, plus the bows from an Imperial camp and Nordic barrow, she appears to be collecting all bows she comes across. There is a hunting bow that's been in her inventory since I got her, but she never uses it, only the better ones that I give her, or she picks up, also, I have never witnessed her picking the bows up, but they were in her inventory nonetheless.