Take a look at this. Not my work but found it interesting.

http://microctworld.net/bvtv-bone-volume-density/

Concepts have different meanings depending on the reference dimensional scale the observation is made.  At the tissue scale, microstructure is explicitly observed and modelled, we talk of BV/TV, and the module of the elasticity of the bone tissue, usually called bulk modulus or tissue modulus, is very constant and independent from BV/TV.

At the organ scale, bone is assumed to be a continuum, and we talk of Young's modulus.  We usually do not use BV/TV here, but the concept of apparent density in all its variations (Ash density, numeral density, apparent density, etc.).

If you want to correlate Bone density to Young's modulus here are some references:

http://www.ncbi.nlm.nih.gov/pubmed/17931759

http://www.ncbi.nlm.nih.gov/pubmed/18606417

Thanks Macro. That makes complete sense.

As correctly pointed out by Prof Viceconti, the first thing to specify here is whether you are referring to the elastic modulus of the "solid" bone tissue or to that of the whole bone structure (either trabecular, cortical, or total). We can call them, for simplicity, "material" modulus and "structural" modulus, respectively.

The "material" (Young's) modulus is proportional to the stiffness of the bone mineralized tissue, and is biologically determined chiefly by the collagen fibers quality, the degree of mineralization, and the crystallinity of the OH-Ap. The "structural" modulus (more properly told, the "structural stiffness") of trabecular, cortical or total bone at the organ level of complexity, defines the load/deformation ratio of the studied structure, and depends on the corresponding tissue modulus and the mass (volume) and spatial distribution of the tissue (trabecular network, cortical shell, whole bone).

Your question faces two mechanical problems that are generally difficult to solve, namely,

1. Both bone "moduli" are highly directional, i.e. they depend strongly on the relationship between the spatial orientation of the collagen fibers (tissue modulus) or of the mineralized tissue (structural modulus), and that of the deforming force acting on the bone.

2. It is very difficult (impossible, I would say) to measure cortical and trabecular bone structural moduli separately for a given bone, because, at the organ level, the modulus of each of these structures depends largely on the way both structures are interconnected and spatially interrelated within the bone.

Thus, if you (independently of the care wou could take in doing it) separate the cortical and trabeculare bone of a femur, you will produce two structures whose moduli have little if any to do with the structural modulus of the whole bone. At the best, you could study the behavior of the separate cortical or trabecular structures as mechanically tested in some specified conditions concerning the directionality of both bone structure and the acting load, and following some specified determination geometry. Obviously, the results of such tests will tell you nothing about the mechanical behavior or properties of the whole femur, regardless of the directions and geometries you had selected for the determinations.

Alternatively, if you test mechanically a whole piece of the femur (say, the neck. or the diaphysis), you will not only be facing the same above problems; in addition, your determination will be again highly affected by the directionality of the loading force and the geometry of the determination.

Furthermore, your question poses a third, extremely complicte problem to deal with. In the specific case of trabecular bone as a separate structure, its "structural" modulus (to which I asume you are making reference in your question) will depend on all the (trabecular) tissue modulus, mass, and spatial distribution. Among these three determinants, what you refer as "BV/TV" is a histomorphometrical indicator of the amount of "solid" bone tissue present within a given volume of whole (trabecular) bone tissue (i.e., inluding pores and medular spaces). In this case, the "structural" modulus will depend on all, "tissue" modulus, BV/TV, and directional relationships between network and loading force. The matter here is how to define a function in which a. "tissue" modulus directionality copes with the directionality of the whole thing you are measuring, b. BV/TV plays a role as a mass indicator for trabecular bone that is very difficult to assess in quantitative terms, and c. you ignore how does the directional relationships between the loading force and the network "most efficient" stress supporting ability play regarding bone strength determination. And,  to the worse, you cannot forget that you would be testing the resistance of a whole piece of bone (organ level), in which both cortical and trabecular stress-supporting ability are involved and combined in a inextricable way.

Regrettably, I have no answer to any of all these three questions.

Perhaps you could find some experimental reference of direct measurements of trabecular bone structural modulus and whole femur strength, and some attempt to correlate both mesurements. If so, you will have to be very careful in interpreting the data as per the above observations.

Sincerely, I think that your question has no question, rather tan having no answer.