Note that the Into approach will avoid cloning[1] the passed in String in the case of Some(string). Assuming getting a String into local_bar is indeed the goal.
If you always need a String -- which from the example it looks like you do -- then just make the caller pass you a string.
It's really not worth the inference and compile-time performance costs, IMHO, if you're just going to force it to be an allocated String anyway.
(Things like &[AsRef<str>] can have their place, as can Into<Cow<str>>, but if you're going to force something into being a full String anyway, just take one.)