Align concentric holes of different sizes in 2 pieces of metal on drill press
Working with my very basic press, I'd clamp the two pieces together very well, and drill all the pilot holes. Then separate the pieces and open out the clearance holes. I wouldn't go straight in with a 6mm drill in steel anyway.
Note that you'll need a little over 6mm for a clearance hole. 6.5mm is common though might be too loose for you. In thin aluminium you might get away with drilling to 6 and forcing the bolt in, but probably not in steel, unless your drill chatters and makes an oversize hole.
When opening out the clearance hole, allow the drill to self centre, i.e. don't clamp it down hard before you start drilling (assuming you're using a normal drill bit and not an end mill). This is where a heavy machine vice or toolmaker's vice is really useful, as a roughly aligned work piece can move a little as the conical tip finds the hole. You can then clamp down the vice if you feel the need.