Since Bounderby is a self-made man, why does he have so much contempt for the working class?

I'm not sure where you are in the novel, but Josiah Bounderby is a fraud and his contempt comes from the realities of his childhood. He's very believable and spends a great amount of time holding himself up the the illusion he's created around himself.

He's a member of the middle class, that is a fact. He also works very hard to make people believe he's worked hard to achieve this position. He's a champion amongst the people because he has gotten where everyone would like to be; he makes things look possible, but that illusion is based on lies. Although he loves what he does, as well as the money it affords him for luxuries, he has no freetime................ this is how he describes his childhood;

' I hadn't a shoe to my foot. As to a stoc king, I didn't know such a thing by name. I passed the day in a ditch, and t he night in a pigsty. ... 'I was born with inflammation of the lungs, and of everything else, I believe, that was capable of inflammation.' ... ' How I fought through it, I don't know,' said Bounderby. 'I was determined, I suppose. I have been a determined character in later life and I suppose I was then. Here I am Mrs. Gradgrind, anyhow, and nobody to thank for my being here, but myself' (Dickens 37).

Bounderby maintains that he fought his way, tooth and nail, to gain his present position. This is a very admirable accomplishment. Everyone takes Bounderby's story for the gospel until his Mother, Mrs. Pegler, uncovers his scheme. She did not abandon him, as he claimed, and he did not work his way up from obscurity. This is what makes Bounderby a believable character. Acceptance is a vital human quality, but admiration is the most sought after. If Bounderby goes by the truth, then he gains acceptance into society. If, however, he concocts this story about fighting his way up from a ditch, then he gains the admiration of his peers.