I'm trying to modulate from the song 7 Years (Gm) to the song Hometown Glory (Bbm). How do I write a something that joins the two?
You could finish the G minor part on Gm! A bar or two on either Cm or just C would sound natural, as it's the cycle of fourths, followed by a bar or two on F(7) again in the cycle, to get in an unobtrusive way into Bbm.
Don't forget the REALLY obvious, uncontrived method. End the first song, go straight into the intro of the next. Gm has plenty in common with Bbm, it won't sound like a wrench, in fact it will sound very pleasant and uplifting. Even if there's no intro and you have to jump straight into singing the first note of the new song, you likely don't need a crutch. It's one note, followed by another note. You've been doing that all night!
You have two really obvious choices that both use the same method to get you from G minor to B♭ minor.
The first is you could write a few measures in G minor and then when ready cadence on an F7 which is the dominant chord of B♭ minor. The second thing you could do is since the relative major of G minor is B♭ major so you could play a few measures in B♭ major then use the F7 in the same way above you will convincingly go to B♭ minor.