Bleaney-Bowers itself describes the magnetic susceptibility rather than the EPR profile. On the other hand, it can still be useful in your situation.

The term 1 / (1 + 1/3exp(-2J/kT)) in BB equation describes the occupancy of the excited triplet state (if J < 0), which is the one responsible for the EPR signal (because the ground singlet state in non-magnetic). Consequently, the intensity of the EPR signal depends linearly on the occupancy of the triplet state, which is obviously connected with the BB equation through the 1 / (1 + 1/3exp(-2J/kT)) term

I would try to fit all the EPR spectra in any manner you like and extract the temperature dependence of the peak intensity. This temperature dependence can easily be fitted by the 1 / (1 + 1/3exp(-2J/kT)) term, which occurs in the BB equation.

As Mikhail described, you need to extract the intensity (I) of your EPR signal at each measured temperature (T) and plot it as I vs T or I*T vs T and fit to the BB model (proportionality constant cannot be directly related to the susceptibility but the shape of the curve is the same). Check this ref, fig 13, for an example in copper acetate: https://www.sciencedirect.com/science/article/pii/S0010854522006026