Bresson was an influence on Eggleston, i think Eggleston met Bresson once and he was rather disparaging of "colour", never meet your heroes!
Obviously in that period (Magnum et al) serious photojournalist worked in B&W, colour was the medium of advertising. Bresson gave up making photographs thinking drawing and painting was a better was to express himself, unfortunately his mark making skills don't have the clarity of his eye! Not unlike Eggleston's forays into music it could be said.
Ernst Haas started using colour in the 50's, realizing it could be as expressive, vital and poetic as B&W.
Of course they're is something powerful about the tones in B&W, the luminosity of a print, stripping away the colour just leaves the essence of the photograph and it's often easier to see how the light effects the surface.
As a kid i used to watch B&W films and not really understand why they were so compelling, i now understand that it was the richness of the tonal range, dynamic compositions and the way the light was used.