How is Cassius angry, bitter, and jealous ?

Cassius is indeed incredibly angry, bitter, and jealous towards Caesar. This is why he joins the plot to assassinate him. Although Brutus may well be motivated by high ideals, Cassius gets involved for purely selfish reasons. And there's no doubt whatsoever that Cassius really does hate Caesar.
His hatred arises largely from his envy of Caesar's exalted position in Rome. Cassius clearly thinks he's just as good, if not better, than Caesar. Why shouldn't he have power instead? Caesar's dictatorship has deprived a lot of noble Romans of what they believe is rightfully theirs, and Cassius is one of them. He thinks that he's entitled by birth to exercise power and influence in Rome, and so he cannot stand to see another man pandering to the mob as he accrues the powers of a king.
But Cassius can't compete with Caesar in terms of greatness, and he knows this deep down inside. So he belittles him, disparaging his ability to swim; making fun of his epilepsy. This is no great man, scoffs Cassius, we—that is, Cassius and Brutus—are better than him. Why should we be slaves of this so-called great man who cried for water after he came down with a fever? Cassius's attitude is contrasted to that of Brutus. Brutus isn't happy about what's happening in Rome, either, but he still professes his love for Caesar as well as his genuine concern over what's best for Rome:

Brutus had rather be a villager
Than to repute himself a son of Rome
Under these hard conditions as this time
Is like to lay upon us. (act 1 scene 2)