I generally only drop benching from a clients program when they are over the 300 lb mark and can do weighted dips with enough weight to make a difference, and their press is where I want it to be in relation to their goals.
It is hard to move the press without bench presses. If the press is gonna be your main focus then I'd rather see you press twice per week rather than db bench, dip, press.
That being said, if I was pressing 137 and bench 190 I would keep benching.