"how high does the bridge for the dog have to be"

High enough so that it will make the string touch the wheel.

The dog string is meant to sound 'ruff' (pardon the pun!) so it needs a fair bit of pressure - this is the reverse of things like violins, etc when too much bowing pressure makes the strings sound 'scratchy', but this is, of course, exactly what the dog string is meant to sound like.

Robin