European bandy wasn't that mature to begin with. There were no national teams until after the WWI and, as a result, international bandy of the 1890s - 1900s revolved around irregular friendlies between various clubs. The Nordic Games, the biggest thing at that time, was also a club tournament.
One of the major obstacles back then was a lack of conventional rules, teams had to chose between Scandinavian, Finnish and Russian codes every time they met. It wasn't until 1955 when the international rules were adopted. In Central Europe, proper "big ice" bandy never even took off, they were playing seven-a-side (or even less, I don't really remember) games on smaller rinks, which is why it was easier for them to adopt the North American game.
I also wouldn't say that bandy evolved into European hockey. It certainly influenced it in many ways in the course of the decades of their coexistence, but both games had their own separate paths of development.