Dry fire as much as you can stand (that will smooth up the trigger, too) with the laser after quadruple checking that the gun is empty of cartridges so the bullet fairy doesn't foul you up. Watch where that little red dot goes when you pull the trigger. Change your trigger finger grip to get the pull you want without waggling the point of aim. I'm a big fan of using the distal joint of the finger (farthest toward the end) because you can feel which side of that joint is pulling most and then adjust so the pull is even.
The BG38 does not shoot to the left all by itself, where'd that come from? Ammo might make a difference but I'd like to see proof of a "design flaw". Besides, it's a point and shoot, up close type of gun. Better to practice that way than to treat it like a target gun which it certainly is not.
If you're using the laser, move its point of aim to coincide with the point of impact or move it so it is exactly parallel to the bullet's windage axis. If you do that, the point of impact should remain less than an inch to the left of the point of aim—like any other laser on the right— and just allow for elevation.