Piano question?!

Piano question?

I need to find the harmonic minor scale whose dominant is Bb (B flat).
Since the dominant note is the fifth note, I counted down to find what minor scale it was and I got E.
To find the key signature for the minor scale, I went up 3 semitones, like i was taught, and the answer I got was that the key signature for e minor was the same key signature for G major.
The KS for G major and e minor is F#...but, the dominant for the scale is Bb.
What did I do wrong?
Thanks.

I'm not sure if this is right but...
instead of counting down 5 notes, try counting down 7 semitones.
for example, you could count down 5 notes from G, and get C. But, you could also count down 5 notes from Gb, and get C also, which would be the wrong answer.
SO, count down 7 ST from Bb, and instead of getting E, you'll get Eb. The KS for that is the same as Gb minor, which includes Bb.
Hope this helps.