So, I have a song (Not to Us, by Chris Tomlin) that I've determined is in the key of B, and is Dorian, since the song contains B (root), a Natural D (Flat 3rd), and a Natural A (a flat 7th) notes in the song. Does this mean the song is in B Dorian, or A Dorian? (since B is the 2nd degree of A)? Also, does this mean that if I want to improv/solo during an instrumental in this song, I can play the Dorian scale starting on B?
You could, but, your Dorian sound may get drowned out because ----- Most Chris Tomlin songs have a bunch of chords in them. [Invalid or Expired Link Removed] Keep reading..... Any time you have a full chord progression the tonal center of the V-I cadence will drown out the modal sound. Yes you played Dorian, but the Dorian sound is wasted with all the chord changes. As mentioned in other posts here - the signature note for Dorrian is the natural 6 note (sound). That sound needs to be dronning in the background for the Dorian sound to sustain. We do that with vamps not chord progressions.
The Dorian sound (mood) does not have time to develop. But, to answer your question; yes you could play Dorian, but, don't count on Dorian's sound coming through, as long as the harmony chords revolve around a V-I cadence.
There are very few places a mode will fit into a bass line. Into a solo, perhaps, if the other guys will move from the V-I cadence to a modal vamp while you are playing your solo. Good luck with that happening.