She was devastated after her birth-son Peter died. When Walter brought back Peter Bishop from the Alternate Universe to cure him of his genetic malady, she was so happy to see "her" son, that Walter realized that he would not be able to return the child to his true father. ("Peter")
Approximately six months later, she struggled to keep the secret from Peter. She used Walter's explanation of Peter's treatment/illness as an alibi for Peter's confusion and memories of the alternate world under Reiden Lake. When Peter finally accepted her as his mother, she could not contain the guilt she felt and coped with excessive alcohol consumption. ("Subject 13")
After Walter was institutionalized in 1991, Elizabeth moved to Allston with her adoptive son because she could not afford the mortgage of their house in Cambridge. She continued to raise Peter until he left home, dropped out of high school and became a gambler.
She committed suicide in the year 2000. Peter, aware of her depression and having forgotten he had come from the other universe, initially interpreted her death as being a result of unable to cope with Walter's incarceration. However, when he learned he was from the other side, Peter realised that she had not been able to live with the guilt of the lies, and convincing him he was her son. ("The Man from the Other Side")
Peter mentions to her counterpart that she was a vegetarian, and that she was wonderful and took care him, although she wasn't "strong" and often sad. ("Over There: Part 1")
Alternate Timeline Edit
Due to the nature of Peter's erasure, Walter's plan to bring the other Peter back was not successful.
Elizabeth still remained depressed over the death of her son and committed suicide from the grief, Walter's own declining mental health and institutionalization after losing two Peters as well as being left alone in the world.
Alternate Version Edit
Elizabeth Bishop (Alternate Universe) is still alive on the other side.