What would you do if you had to bridge a tri-tone interval. Like from the Key of E to the key of Bb? I'm specifically thinking about from Israel & New Breed's "Lord You Are Good" ending in E into William Murphy's "Lord You Are Awesome" in Bb?
In that situation, I would turn the E major chord into a C major chord keeping the E in the bass, go to F major chord with F in the bass (you're now on 5 of Bb). Then maybe another chord to establish Bb as the new key, then straight to the Bb major chord.
E / E-G#-B ending chord for "Lord You Are Good"
E / C-E-G modulation chord from E to Bb
F / C-F-A
F / Eb-G-Bb-D
Bb / F-Bb-D
Every key is related in some form or fashion. So, there's always a way to get from anywhere to anywhere. Some are smooth, some are funky, but there is a way.