Some magnetic early B-type stars display H alpha emission originating in their Centrifugal Magnetospheres (CMs). To determine the rotational and magnetic properties necessary for the onset of emission, we analyzed a large spectropolarimetric dataset for a sample of 51 B5-B0 magnetic stars. New rotational periods were found for 15 stars. We determined physical parameters, dipolar magnetic field strengths, magnetospheric parameters, and magnetic braking timescales. H alpha-bright stars are more rapidly rotating, more strongly magnetized, and younger than the overall population. We use the high sensitivity of magnetic braking to the mass-loss rate to test the predictions of Vink et al. (2001) and Krti. cka (2014) by comparing ages t to maximum spindown ages t(S, max). For stars with M-* < 10 M-circle dot this comparison favours the Krti. cka recipe. For the most massive stars, both prescriptions yield t << t(S, max), a discrepancy which is difficult to explain via incorrect mass-loss rates alone.