When transposing a song to a new key, do I use a 'sharp' or a 'flat'?

I am building a program which will automatically transpose guitar chords from one key to any other desired key. One thing that is holding me up is the following scenario.

If I have a song in the key of G and I want to transpose it to the key of Bb it seems like it would be equally valid transpose it into the key of A# since they are the same note on the fretboard.

How do I know whether a song key should be labelled as ‘sharp’ or ‘flat’?

It seems like I see songs in ‘Bb’ much more often than ‘A#’. Why is that?

Thanks for your help. I play music by ear and haven’t had much of any formal training.