Common sense will help.
In NY and I assume in all places, the shooter is responsible for where his bullet winds up. Even in the few cases where an absurdly weird and totally unpredictable event intervenes... the shooter is responsible but the penalty may be lessened by the presiding judge. No matter what you build, if a shot goes astray and there is any reason for anyone to complain, you can bet that here in Obamaland you'll be taken to task over it.
I wouldn't let it keep you up at night... you drive a car, right? Much, much more likely that you'll be in a wreck that will result in a lawsuit. I'm not sure how much if at all, personal liability insurance would cover a shooting accident. Do you know?
Given that you can't anticipate every errant shot (holding the gun off to one side checking the safety and hitting the trigger.... ooops.) I've thought about this too and decided it comes down to; how good a shot are you? If you never miss then a bucket full of dirt is good enough for all shots down near the ground. How high will your targets be? If you intend to shoot off-hand and at up elevations, the dirt pile height will depend on the slump coefficient of the soil you use and will errode over time so maintenance will be a factor (have extra soil piled near by to add to the backstop as needed).
In short; I've never come up with a good answer and this could lead to in-action for ever. In my case I have a place that affords us a 100 yard range, down in a stream gully (the flat flood plain alongside the stream and so, unusable for maybe three or four days / year) it has a natural 8' bank backstop at an abrupt curve in the stream and, the way-down-range objects are trees (flat forested, uninhabited lands for over a mile).
If I want a long range or if I want to shoot anywhere else other than that stream gully... I have to do what responsible men in America have done for over two centuries: I make an on-the-spot determination of the conditions before I pull the trigger. That includes having to pass up a 30-point buck if he's on the ridge above me with nothing but sky beyond him.
Sorry I can't be of more help... that question plagues me too.