We study the role of the bias current sweep rate in measurements of polarization switching (PS) of vertical-cavity surface-emitting lasers (VCSELs). We show that the polarization-resolved L-I (light-intensity) curve depends on the current sweep rate. As the current sweep rate increases, the PS occurs at higher bias currents for upward scans and at lower bias currents for downward scans. We also show that the delay of the dynamical bifurcation follows a power law relationship with the frequency of the ramp, in good agreement with recent theoretical predictions.