I spent a while trying to figure this out. The web is abound with photographers justifying a use of a 35mm or 50mm lens, but I couldn't find a solid reason why Bresson preferred 50mm until I came across this interview in the New York Times:
Q. Why the 50-millimeter lens?
A. It corresponds to a certain vision and at the same time has enough depth of focus, a thing you don’t have in longer lenses. I worked with a 90. It cuts much of the foreground if you take a landscape, but if people are running at you, there is no depth of focus. The 35 is splendid when needed, but extremely difficult to use if you want precision in composition. There are too many elements, and something is always in the wrong place. It is a beautiful lens at times when needed by what you see. But very often it is used by people who want to shout. Because you have a distortion, you have somebody in the foreground and it gives an effect. But I don’t like effects. There is something aggressive, and I don’t like that. Because when you shout, it is usually because you are short of arguments.
Along with technical qualities of a 50mm lens Bresson didn't like distortion, he didn't like to "shout."
Remember that Henri Cartier-Bresson started and ended his life as a painter. The kind of distortion with even a 35mm Leica lens would be very difficult to achieve and rather ugly in a painting. The 50mm lens is the widest lens that allows you to take pictures that look like paintings without distortion.
I think that's why Bresson preferred the 50mm. Of course you can just read the New York Times interview yourself or make up your own ideas on why he preferred it.
I'll leave you with one more link: a compelling argument that today the Leica is designed for 35mm lenses. I've started shooting a 35mm lens alongside my 50mm lens, it helps me get a lot of shots I wouldn't otherwise take, but having grown up on 50mm I'm not a fan of the distortion.
"That's why he only shot with one lens his whole career: it's all he could afford, and he came from a very wealthy family!" ↩
"Sure Henri cartier-Bresson shot with a 50mm lens but I don’t recommend the focal length. Why? A friend recently made a point that interested me. Henri cartier-Bresson was shooting in the mid 20th century, where streets weren’t as narrow or crowded as nowadays. Therefore a 50mm would have probably served him pretty well. However nowadays if you live in the city, things are always jam packed. I would state that the 35mm is equivalent today to the 50mm hcb used in his time." ↩