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We study the origin of the observed bi-stability jump in the terminal velocity of the winds of supergiants near spectral type B1. To this purpose, we have calculated a grid of wind models and mass-loss rates for these stars. The models show that the mass-loss rate 'jumps' by a factor of five around spectral type B1. Up to now, a theoretical explanation of the observed bi-stability jump was not yet provided by radiation driven wind theory. The models demonstrate that the subsonic part of the wind is dominated by the line acceleration due to Fe. The elements C, N and O are important line drivers in the supersonic part of the wind. We demonstrate that the mass-loss rate 'jumps' due to an increase in the line acceleration of Fe III below the sonic point. Finally, we discuss the possible role of the bi-stability jump on the mass loss during typical variations of Luminous Blue Variable stars.