Context : Variable B supergiants ( BSGs ) constitute a heterogeneous group of stars with complex photometric and spectroscopic behaviours . They exhibit mass-loss variations and experience different types of oscillation modes , and there is growing evidence that variable stellar winds and photospheric pulsations are closely related . Aims : To discuss the wind properties and variability of evolved B-type stars , we derive new stellar and wind parameters for a sample of 19 Galactic BSGs by fitting theoretical line profiles of H , He , and Si to the observed ones and compare them with previous determinations . Methods : The synthetic line profiles are computed with the non-local thermodynamic equilibrium ( NLTE ) atmosphere code FASTWIND , with a \beta -law for hydrodynamics . Results : The mass-loss rate of three stars has been obtained for the first time . The global properties of stellar winds of mid/late B supergiants are well represented by a \beta -law with \beta > 2 . All stars follow the known empirical wind momentum–luminosity relationships , and the late BSGs show the trend of the mid BSGs . HD 75149 and HD 99953 display significant changes in the shape and intensity of the H \alpha line ( from a pure absorption to a P Cygni profile , and vice versa ) . These stars have mass-loss variations of almost a factor of 2.8 . A comparison among mass-loss rates from the literature reveals discrepancies of a factor of 1 to 7 . This large variation is a consequence of the uncertainties in the determination of the stellar radius . Therefore , for a reliable comparison of these values we used the invariant parameter Q _ { r } . Based on this parameter , we find an empirical relationship that associates the amplitude of mass-loss variations with photometric/spectroscopic variability on timescales of tens of days . We find that stars located on the cool side of the bi-stability jump show a decrease in the ratio V _ { \infty } / V _ { esc } , while their corresponding mass-loss rates are similar to or lower than the values found for stars on the hot side . Particularly , for those variable stars a decrease in V _ { \infty } / V _ { esc } is accompanied by a decrease in \dot { M } . Conclusions : Our results also suggest that radial pulsation modes with periods longer than 6 days might be responsible for the wind variability in the mid/late-type BSGs . These radial modes might be identified with strange modes , which are known to facilitate ( enhanced ) mass loss . On the other hand , we propose that the wind behaviour of stars on the cool side of the bi-stability jump could fit with predictions of the \delta - slow hydrodynamics solution for radiation-driven winds with highly variable ionization .