The fixed-point structure of the 2D 3-state random-bond Potts model wi
th a bimodal (+/-J) distribution of couplings is fully determined usin
g numerical renormalization group techniques. Along the paramagnet-to-
ferromagnet critical line we find a total of four distinct fixed point
s: i) the pure critical fixed point, ii) the critical fixed point for
the random-bond, but unfrustrated, ferromagnet, iii) a bicritical fixe
d point analogous to the bicritical Nishimori fixed point found in the
random-bond frustrated Ising model, and iv) the zero-temperature spin
-glass-to-ferromagnet critical fixed point. Estimates of the associate
d critical exponents are given for the various fixed points.