Popular music, when it does have key changes, rarely has any kind of extended modulation like classical music but rather tends to jump directly to the new key. And the key change is rarely to things like the dominant.
A jump from a minor key to the relative major is probably the most common key change in popular music. My guess is the second most common would be the change up a tone, often at the end of a song or after the bridge to add excitement as the song reaches its climax.
But a third that you do see (that, like the minor/relative major change is more about contrast than adding excitement) is a change to the relative major of the parallel minor (e.g. C major to Eb major or G major to Bb major). I've written a couple of songs that make this change between verse and chorus. Coming back to the original tonal centre after the change can give a real sense of "returning" after a detour.
Better Man seems to make use of this same temporary key change to emphasize the detour that is the bridge and give it more of a contrast.