Unfortunately, my own math skills aren't good enough to get you an answer you could write down. Maybe a physicist would be able to help you? The only way I know how to calculate it is to write a computer simulation to calculate the actual 3D shapes of the magnetic fields near a quadrupole magnet including the negative magnetic susceptibility of the bismuth. Even a simplified 2D version that you might be able to calculate with a big spreadsheet (finite difference method solutions to magnetostatics) wouldn't be easy to explain (it would be clear that someone else had set up the calculation, which takes the fun out of any experiment), and it wouldn't even give the right answer. That was why I suggested measuring the force instead. Then you wouldn't have to make any approximations at all. Sorry I couldn't be more help...