Correct me if I'm wrong, but I believe a fully charged (or near-fully charged) launched Gyro breaks through Bowser's Flame Breath? I remember it happening in a match I had against the Bowz. If that's true, that means that both of our projectiles can bypass Bowser's only anti-zoning tool, which def helps us a lot.
Other than that, this MU isn't too complicated. Obviously, Bowz has lots of trouble with getting zoned out in general, not to mention Beep Boop works wonders at KO%. For the most part, our aerials either outspeed or flat-out beat Bowz's entire aerial kit, not to mention his air speed is pretty low, so we win in the air. So yeah, we definitely win by a large margin, probably 60:40 or 65:35 more or less.