Like plastic black guns, even not dangerous training swords should be carried and showed in public with "caution"... I would never use my bow out of a dedicated place (or backyard - which is quite appropriated). Not saying it is absolutely and ever wrong, just saying it can avoid trouble, for sure.
Just like a few years ago when the IRA was attacking and bombing us, the public here have again been asked to be vigilant so it makes sense not to prat around in public with anything resembling a weapon.