Is there a term for the stereotypical Japanese ghost girl with a white dress and long black hair that mostly covers her face?

They are called onryō.

In traditional beliefs of Japan and in literature, onryō (怨霊, literally "vengeful spirit", sometimes rendered "wrathful spirit") refers to a ghost (yurei) believed capable of causing harm in the world of the living, ailing or killing enemies, or even causing natural disasters to exact vengeance to redress the wrongs it received while alive.

A ghost costume consisted of three main elements:

• White burial kimono, shiroshōzoku (白装束?) or shinishōzoku (死に装束?)
• Wild, unkempt long black hair
• Face make-up consisting of white foundation...

http://en.wikipedia.org/wiki/Onry%C5%8D

Tvtropes describes as Stringy-Haired Ghost Girl and also mentions onryo:

An entity often seen in Japanese horror movies is a ghost, usually that of a young woman, with long, stringy black hair that covers her face, clad in a white burial kimono or shroud. Her face itself is often quite ghastly to look upon. In some cases, this type of ghost will appear with a pair of ghostly blue flames hovering around her.

This is actually a type of ghost known as an onryo, the ghost of a young woman who was greatly wronged by a man in life and now seeks vengeance on the living.