How would I write a song in Locrian of C. In sheet music would that be written in the key of C. Or would I write it in B minor / major?
If B, I'm guessing the way I would choose between the minor and major would be by the other chords in the song.
Since the root, or tonic of Locrian of C is B, it could be written with the key sig. of 5# for B maj., or 2# for B min., more likely the latter, as Locrian is more minor than major. That would mean putting naturals on F and C, which would probably encourage a reader to think it's modal, and Locrian.
Don't know why you suggest B#, as it's enharmonically C, and if you wanted to write the piece in C, then a C key sig. would just about suffice. B# isn't in it.
It could always just be written with a C major key sig., as that's the mother key, but I'd tend to write a little note at the top pertaining to Locrian, or even include the word within its title...bit like 'Symphony in Eb'.
Actually, the standard key signature for any mode comprises the sharps or flats (or combination of both - see some of Bartók's pieces) that define the mode. In the case of B Locrian, that means an empty key signature, as B Locrian uses the same heptatonic collection as C major/A minor.
Key signatures don't really exist to specify the key (despite the name), at least in part because the same signature can be shared by more than one key; they're a notational convenience to streamline the writing of notes that are normally going to be flatted or sharped within the prevailing tonic and mode. Even in major and minor, you have to look at the progressions, melodic figures and cadences to determine the key, not just the note collection.