I like how you counted 4 notes up the scale from G to C, and 5 notes up the scale from G to D. That's what scales are all about.
This is a really smart wrong answer, I kind of want to give you partial credit.
G Major chord = G B D
G Minor chord = G Bb D
You have correctly identified that Bb is the "defining" note of G Minor, that makes it sound different than G Major. So logically, we are going to be using Bb in our G Minor Blues song. Great work!
The only piece of information you are missing is that "minor blues songs" are similar to "major blues songs" that use the I, IV, V chords. The difference is that they are minor chords instead of major chords. We indicate this with lower case Roman numerals: I, IV, V for major and i, iv, v for minor.
In conclusion a "G Minor Blues" song uses the chords Gmin, Cmin, Dmin (or variations thereof).
Famous songs you might know, compare the sound of SRV's "Pride and Joy" (major blues) with BB King's "The Thrill is Gone" (minor blues).