Help! Need a little guitar tip?

I'm trying to perfect my guitar play of this song: Ross Copperman- They'll Never Know. It has fairly basic chords, but I have trouble with transitioning between the resounding E maj chord and the A maj barre chord in the chorus. I also have the same problem between the E maj chord and the B maj barre chord found in the verse. So my question is! Are there any good ways to transition between regular chords and bar chords (that appear higher on the neck)? Or is this something that I'm going to have to practice over and over again until I get it down? FYI, I'm going to be singing/playing this song for a talent show, so I don't want there to be awkward pauses in the song while I'm trying to get my fingering straight. Thanks for the help!