Nathan East recorded this with a 5 string bass but in this video lesson, I teach you the basic groove on a 4 string. It's a good one to learn because it's the same four chords over and over again.
This song uses a iv VI i VII chord progression in the key of F# natural minor (Bm, D, F#m, E). I explain that in the video but what it means is that the notes of the F# natural minor scale fit over all the chords in this song.
That is the secret to improvising when playing a song. You can also create basslines with ease if you know this.
For more basslines head over here.