The elastic properties of crystalline metals scale with their valence electron density. Similar observations have been made for metallic glasses. However, for metallic glasses where covalent bonding predominates, such as metalloid metallic glasses, this relationship appears to break down. At present, the reasons for this are not understood. Using high energy x-ray diffraction analysis of melt spun and thin film metallic glasses combined with density functional theory based molecular dynamics simulations, we show that the physical origin of the ultrahigh stiffness in both metalloid and non-metalloid metallic glasses is best understood in terms of the bond energy density. Using the bond energy density as novel materials design criterion for ultra-stiff metallic glasses, we are able to predict a Co$\mathrm{<mrow\; data-mjx-texclass="ORD">33.0</mrow>}$Ta$\mathrm{<mrow\; data-mjx-texclass="ORD">3.5</mrow>}$B$\mathrm{<mrow\; data-mjx-texclass="ORD">63.5</mrow>}$ short range ordered material by density functional theory based molecular dynamics simulations with a high bond energy density of 0.94 eV Å$\mathrm{<mrow\; data-mjx-texclass="ORD">-3</mrow>}$ and a bulk modulus of 263 GPa, which is 17% greater than the stiffest Co-B based metallic glasses reported in literature.