Warding helps you, and more importantly in Bronze, your team-mates not dying. If you ward more, maybe your midlaner will not stupidly chase this tank with 15% HP into the enemy jungle and get ambushed by their whole team, because he can see them on the map.
Warding doesn't directly win games, it just reduces your team stupidity to manage-able levels. And that's why warding is especially important in Bronze. In higher ELO, you don't need to see an enemy to guess he's probably ambushing you in the Fog of War, and to not follow a Tank. In Bronze, you won't ask yourself if it's a good idea or not: you see a low life enemy, you chase him.
So ward, it saves life, and so it wins games. Even in Bronze.