When your riding a bike you get on from whatever side feels best and casting is exactly the same, you cast whatever way is best and most comfortable to YOU.
With the exception of possibly 2 or 3 people, I've been using a bait caster longer than anyone on this board and I'm pretty darned good at it too,
I'm right handed and cast with my right hand on the reel. I then switch and hold the rod with my left hand and crank with my right. It's worked great for me for many many years yet some folks will still tell me I'm doing it wrong.
If it works for YOU...your doing it right.