Someone who is arrogant and pompous can be described as swaggering. A swaggering bully strides confidently up to the front of the line, pushing other people out of his way, certain he deserves to be first on the airplane.
Use the adjective swaggering to describe someone with little regard for other people's feelings and an inflated sense of their own self-worth. You shyly start to raise your hand in English class, only to hear a swaggering classmate loudly call out the wrong answer. Swaggering comes from the verb swagger, "strut insolently," one of those English words famous for being coined by Shakespeare.