How do I transpose from B-flat major to A-flat minor?

Normally a Major transposes to another Major and a minor to a minor. Do you have an example of before and after appearances of what you want to achieve? Are you trying to alter the tone of a Major piece to make it sound like it is a minor or just move the notes' pitches?

Tools>Transpose
Transpose Chromatically, Closest, Select Cb Major / Ab minor
Works for me

Some things to think about.

I assume you are trying to take a tune in major and give it a minor feel. This doesn't always work as well as you might want.
However consider these steps. Basically, You might think of Ab minor as being a step below Bb major. If that is true, The final chord of a piece in Bb major is Bb major. And Ab minor for a piece in Ab minor. So the initial transposition would be down a major second. Change the key to Ab minor, and delete all the resulting natural signs. But there is more to it then that. To help give a minor feel, you may need to make Gb into the Ab minor leading tone, G natural. Sometimes even Eb, also.
As already stated, transposition is major to major and minor to minor. You have to tweak a few things to get from one mode to the other.

https://musescore.com/user/35880724/scores/19845958

So one way to get from B-flat major to A-flat minor:

• transpose your B♭piece to C♭. Then drag the notes as shown in the sample score.