I agree with gwolf about the strength of the core, it's insignificant in compression (bearing).
I'm not familiar with Hysol 934 as a potting compound, but let me share this:
In-plane load in your bushing will be transfered to the skins by two mechanisms; bearing into the skins, and shear between the potting compound and the skins.
The ability of the skin to resist the bearing load from the bushing is suspect. It requires the potting compound to sufficiently restrain the skin from buckling/wrinkling/ripping (assuming the skins are thin), and for everything to stay planar as load increases. In practice, they don't do this very well. You would be wise to disregard this component.
The second mechanism, shear between the potting compound and the skins is your primary load path. The difficulty is that your allowables for this are extremely process-sensitive. You have to undercut the core with some sort of fly-cutter, and have good surface prep for your potting compound to adhere well. If you know the shear allowable for your potting compound/skin combination, your shear allowable, based on area, should have a significant knock-down factor applied (like at least 50%) unless some testing can be done to determine your allowables.
My experience with the FAA is that you will need to test a minimum of 12 samples to get approved 'A' and 'B' basis allowables. More is always better.
With respect to gwolf, I personally think that an FEM is inappropriate for this application.
SuperStress