Is there a particular bacteria that causes itchiness?

Maybe. There has been some published research in regards to streptococcus, staphylococcus causing itching, acting as a "super antigen" (causing activation of white blood cells by an alternate path). However antibacterial treatment has not shown in the majority of cases to cure the itching.
Maybe. Interesting question. Staphylococcus infection of eczematous skin is certainly associated with increased itchiness. But its not clear if the bacteria increases itchiness or simply exploits the skin injured by scratching to cause a secondary infection.