Bb Dorian sounds like a minor chord with the window open: dark and warm at the bottom, with one bright note letting the light in. It is a minor scale, so it never sounds cheerful, but it rarely sounds sad either. It sounds soulful, a little funky, and quietly hopeful, which is why melody writers keep coming back to it.
Here are the notes of Bb Dorian: Bb, C, Db, Eb, F, G, Ab. Play them on a piano starting from Bb and you'll use four black keys (Bb, Db, Eb, Ab) and three white keys (C, F, G).
Why Db and not C#? Why Ab and not G#? A scale uses each letter name exactly once, in order. Starting on B (as Bb), we need one of each: B, C, D, E, F, G, A. So the third note has to be some kind of D, and the seventh has to be some kind of A. That gives us Db and Ab. Each spelling also tells you its job at a glance: Db is the minor third, Ab is the minor seventh.
You may sometimes see this scale written as A# Dorian. It sounds exactly the same, but spelling it that way takes 8 sharps, including double sharps, which is a lot of reading for no gain. Bb is simply the friendlier name for the same sounds, so don't worry if you run into the other one.
Music moves in steps. A half step is the smallest step in Western music, like moving from one piano key to the very next one, black or white. A whole step is two half steps. Dorian follows this pattern: W - H - W - W - W - H - W.
Walk it from Bb: a whole step to C, a half step to Db, whole steps to Eb, F and G, a half step to Ab, and a whole step back home to Bb.
Those are the same notes as Ab major (Ab, Bb, C, Db, Eb, F, G), so Bb Dorian shares its key signature, the group of sharps or flats written at the start of every line of sheet music. Here that's 4 flats: Bb, Eb, Ab and Db. The difference is where the music feels at rest. In Ab major, Ab is home. In Bb Dorian, everything leans toward Bb.
As a formula, measured against the root, the scale is 1, 2, b3, 4, 5, 6, b7. The b3 (Db) makes it minor. The natural 6 (G) is the twist.
For a melody writer, every note has a personality. In Bb Dorian, think of them in three groups.
Bb, Db and F spell the Bbm chord, the home chord. A phrase that ends on any of them feels settled. Bb is the most final, F is open and calm, and Db is the most emotional of the three, that dark minor color.
C sits between Bb and Db and almost always wants to fall to Bb or rise to Db. Eb tends to drift down to Db or up to F. Ab, a whole step below the root, gives a soft, bluesy pull back up to Bb. It doesn't tug as hard as the leading tone in a major key, which is part of why Dorian sounds relaxed rather than urgent.
G is the note that makes this Dorian. In an ordinary natural minor scale on Bb, you'd find Gb there instead. The G, a major sixth above the root, lifts the mood. Sing Bb, Db, F, then G, and listen for that little brightening, like a cloud thinning out. Let G show up on a strong beat or a long note and the listener hears Dorian immediately. Hide it in a quick run and the tune just sounds like generic minor.
Building chords from each note of the scale gives you this family:
Notice the IV chord is major: Eb. That's because it contains G, the color note. Rocking between Bbm7 and Eb7, two bars each, is the classic Dorian vamp heard all over soul, funk and modal jazz. Miles Davis's "So What" lives in this mode, though in a different key. For a longer loop, try Bbm - Cm - Db - Eb, which climbs straight up the scale and lands on that bright major IV before turning around.
Over the Bbm7 to Eb7 vamp, sing or play this:
Bb - Db - Eb - F ... G (hold) - F - Eb - Db ... C - Bb (hold)
The first phrase climbs and lands on G just as the Eb7 chord arrives, so the color note and the chord that carries it hit together. The second phrase walks back down and settles on Bb, with C leaning into it. Change the rhythm, repeat the first half twice, add a jump from F up to Ab. As long as G gets a moment in the spotlight and you come home to Bb, it will sound unmistakably Dorian.
Your home base for Bb is the low E string at fret 6 (and 18 up high), or the A string at fret 1 (and 13). The fret-6 root sits comfortably under the hand, so play the scale from there and find G, the color note, in each octave. Then play the tune above over a looped Bbm7 to Eb7 and aim your bends and long notes at G.
Record yourself holding a Bbm chord for a minute. Over it, hum just three notes, F, G and F, in different rhythms. Then swap G for Gb and hum the same thing. That single half step is the whole difference between Dorian and plain minor, and once your ear catches it, you'll hear it everywhere.
For the bigger picture, read The Dorian Mode.