Zirconium (Zr) has properties conducive to nuclear applications and exhibits complex behavior at high pressure with respect to the effects of impurities, deviatoric stress, kinetics, and grain growth which makes it scientifically interesting. Here, we present experimental results on the 300 K equation of state of ultra-high purity Zr obtained using the diamond-anvil cell coupled with synchrotron-based x-ray diffraction and electrical resistance measurements. Based on quasi-hydrostatic room-temperature compression in helium to pressure P = 69.4(2) GPa, we constrain the bulk modulus and its pressure derivative of body-centered cubic (bcc) β-Zr to be K = 224(2) GPa and K' = 2.6(1) at P = 37.0(1) GPa. A Monte Carlo approach was developed to accurately quantify the uncertainties in K and K'. In the Monte Carlo simulations, both the unit-cell volume and pressure vary according to their experimental uncertainty. Our high-pressure studies do not indicate additional isostructural volume collapse in the bcc phase of Zr in the 56-58 GPa pressure range.