I have looked at how BiaB transposes minor keys and I have found that the rules it uses are exactly the same as for the relative major (the key with the same number of sharps or flats).

(The following issue applies when transposing notation for Bb and Eb instruments. It does not always apply when transposing a song while still displaying it in concert key)

Those rules do not take into account the raised seventh of the harmonic minor. A diminished seventh chord can be built starting on the raised seventh of a minor key, and this can be a substitute for the V7(b9). Unfortunately, anytime the raised seventh of a minor key occurs on a "black key" BiaB call it a flat intead of a sharp. (A flat tonic instead of a raised seven.)

A strict spelling of diminished seventh chords by thirds (rather than by enharmonics) always results in double flat chord tones when the root is a flat. Starting on a sharp results in chord tones that are naturals.

Following is what BiaB gives for dim7 chords, followed by what they should be -- both spelled by thirds (BiaB will never display double flats, but this is to show why diminished chords should never start on flats. That is going to be one of the first improvements that I suggest.)

Key of Amin. Abdim7 - spelled by thirds this would be Ab-Cb-Ebb-Gbb. It should be G#dim7 = G#-B-D-F (much better)
Key of Dmin. Dbdim7 = Db-Fb-Abb-Cbb. Should be C#dim7 = C#-E-G-Bb.
Key of Emin. Ebdim7 = Eb-Gb-Bbb-Dbb. Should be D#dim7 = D#-F#-A-C.
Key of Gmin. Gbdim7 = Gb-Bbb-Dbb-Fbb. Should be F#dim7 = F#-A-C-Eb.
Key of Bmin. Bbdim7 = Bb-Db-Fb-Abb. Should be A#dim7 = A#-C#-E-G.