A critical need exists for new imaging tools to more accurately characterize bone quality beyond the conventional modalities of dual energy X-ray absorptiometry (DXA), ultrasound speed of sound, and broadband attenuation measurements. In this paper we investigate the microwave dielectric properties of ex vivo trabecular bone with respect to bulk density measures. We exploit a variation in our tomographic imaging system in conjunction with a new soft prior regularization scheme that allows us to accurately recover the dielectric properties of small, regularly shaped and previously spatially defined volumes. We studied six excised porcine bone samples from which we extracted cylindrically shaped trabecular specimens from the femoral heads and carefully demarrowed each preparation. The samples were subsequently treated in an acid bath to incrementally remove volumes of hydroxyapatite, and we tested them with both the microwave measurement system and a micro-CT scanner. The measurements were performed at five density levels for each sample. The results show a strong correlation between both the permittivity and conductivity and bone volume fraction and suggest that microwave imaging may be a good candidate for evaluating overall bone health.