So, the strain in the perpendicular direction is equal to the change in diameter divided by the original diameter,
(10.0328 mm - 10.0000 mm) / 10.0000 mm = 0.00328
We calculated the strain in the direction of loading above; that makes the Poisson ratio
nu = -0.00328 / 0.01146 = -0.0286
Again, it's negative, where most materials (including steel) are typically positive. So that's a little bit of a strange result from the test.
Now, bulk modulus measures the resistance to uniform, hydrostatic compression. Imagine dropping your sample to the bottom of the ocean, where it would be squeezed uniformly on all sides by the pressure. The bulk modulus is equal to the pressure required to shrink the volume by a factor of 1 / e, where e is the base of the natural logarithm. Because it's related to the change in three dimensions, we can calculate it from the Young's modulus and the Poisson ratio, using
K = E / (3(1-2nu))
K = 200 GPa / (3(1-2*-0.0286))
K = 63.06 GPa
A couple of notes - as long as the deformations are small, the engineering and true forms of stress and strain are very close to identical. 5% strain is often used as a practical limit. Also, recall that we assumed the deformation was elastic. Since you say it's steel, and we calculate a stress of 2.3 GPa, that's probably not a very good assumption. Most steels have yield strengths much lower than this, although there are a few that reach this value. But, of course, since your Poisson ratio is negative, we're probably not dealing with a real material, anyway. (Certain arrangements of a material's microstructure can result in negative Poisson ratio on a macro scale. See http://silver.neep.wisc.edu/~lakes/Poiss… )
I hope that helps!