Note that NEC is 18" deep to top of NM conduit, or 24" when direct buried. Hence if you are going DB I believe you are looking at 24".Your post got me thinking. I need to bury electric wire 18" deep minimum for about a 200 foot run. Does anyone bury wire this way? or would it tear up the insulation? I don't remember the exact wire spec, but it is buriable 4-8 wire.
That said, you can't pull DB wire with a plow, it has to be trenched in. And if you are opening a trench, I'd advise you put schedule 40 non-metallic conduit in the hole, and then pull wire through it. The added cost is minimal, you don't have to dig as deep, it affords more protection, and if anything ever happens you can just pull a new line through the conduit.
Wrooster