Inspector Bucket is one of the first ever police detectives. Seriously. He sets the tone for the police detectives to come. In Bleak House, Bucket is the hub of the novel's thinking about detection.
One cool thing about Bucket is how much detail Dickens gives us about his working style. Procedure and technique are always interesting, and here we get to explore them to the fullest. First and foremost, Bucket is a people person. He is an amazing reader of everyone he meets, able to quickly understand body language and make the correct snap judgment about how to approach any given person. Not only that, but his behavior is totally flexible and adaptable to any situation. For example, look at the difference between the family-friendly way he talks to the Bagnets when secretly arresting George, the deferential and just-the-facts style he uses with Sir Dedlock, and the drinks-are-on-me good-time-guy persona he adopts when asking about Lady Dedlock at the travelers' inns. Because he is so disarming and chummy, Bucket frequently gets people to admit things to him they wouldn't give up under more hostile interrogation.
What do we make of this method of investigation? In the novel, it seems to be viewed as a generally moral and honest way of going about his business. He's not a spy, secretly watching the unaware (like Tulkinghorn or Mrs. Snagsby). Nor does he skulk around collecting inanimate objects as evidence behind peoples' backs (like Smallweed or Krook). Instead, his detection is completely out in the open – something the novel seems to think is important. Even when he uses trickery to get his way (like his doctor disguise to get at Gridley at Mr. George's place) or when he is working for some seriously evil people (he gets involved in the whole mess because Tulkinghorn brings him in) the people he deals with are forced to admit that he's not really a bad guy. Most of the time, he comes across as noble and trustworthy.
Another key thing about Bucket is that he never works alone. Sometimes his team is all pro (check out the web of policemen who work in combination to pinpoint Lady Dedlock's location). Sometimes he works with some shady characters like Tulkinghorn to get the necessary details. And sometimes he uses the help of amateurs to move the case along (always remember the awesome Mrs. Bucket and her capture of Hortense, the murderous maid). He is truly able to have a good working relationship – to create a team – out of any collection of people. This separates him from those who do their detective work alone (Tulkinghorn, primarily), or those who can't pull it together enough for teamwork (the Smallweeds, who sell each other out for a measly twenty pounds). Why do you think Bucket's ability to play well with others is so important in this novel?