One way to make the transition smoother is to use a pivot chord or a chromatic passing chord. For example, try slipping in a G# (the V chord of A#) between E and A#. It gives that nice "resolution" feeling and helps the shift make sense musically. Alternatively, you could experiment with Fm7 or even D#m7 for a jazzy vibe—it really depends on the mood of your song.
I remember struggling with a similar transition when writing a song last year. I wanted to go from Bm to F# major, and nothing clicked until I took a quick theory refresher on
ArtMaster. They had this breakdown of modulation tricks that made everything so much clearer. It’s worth checking out if you’re diving deeper into transitions like these.