As I am currently reading about Bismarck in school, it surprises me that an aristrocratic ruler like Wilhelm was so willing to do Bismarcks biddings, and in essence allow the chancellor to reign free. Why was that?
I'm a bit late to this question, but I'll answer it anyway.
When Wilhelm I first came to power, there was a situation with the Liberal legislators of the Prussian diet when the monarchy wanted to pass legislation to reorganize the Prussian military. Wilhelm I was hesitant to appoint Bismarck, but was convinced he was a skilled enough politician to push the legislation through.
Bismarck succeeded and continued to earn victories for Wilhelm I against legislators. He ended the budget deadlock and used his powers of persuasion to build a strong alliance with the King.
This led him to become the Chancellor of the German Empire.