http://msdn.microsoft.com/en-us/library/windows/desktop/cc308048(v=vs.85).aspx
Depending on whether your depth buffer is UNORM or floating point varies the meaning of the number. In most cases you're just looking for the smallest possible value that gets rid of your z-fighting rather than any specific value. Small values are a small bias, large values are a large bias, but how that equates to a shift numerically depends on the format of your depth buffer.
As for the values you've tried, anything less than 1 would have rounded to zero and had no effect. 1, 10, 1000 may simply not have been enough to fix the issue. In the case of a D24 UNORM depth buffer, the formula would suggest a depth bias of 1000 would offset depth by: 1000 * (1 / 2^24), which equals 0.0000596, a not very significant shift in z-buffering terms.
Does a large value of 100,000 or 1,000,000 fix the z-fighting?