Grammatically fine. I would change 'the promise' to 'her promise' and change 'during' to 'for': 'She wanted to keep her promise to love Bob for all her life in good times and in bad times.' The phrase often used is 'I promise to love you through the good times and bad' - but that is a stylistic choice.

I am writing a short story about a couple whose name are Bob and Beth . I'm writing a short story about a couple called Bob and Beth.> the story is called " Bob and Beth" ?? Bob had hurt Beth's feeling , and she was indignant WITH Bob's attitude , so she decided to leave him / to be seperated from him .But, Beth thought her decision over , and she decided to give up on her earlier decision. In this context I wrote this : Beth finally understood that her love for Bob was more important than feeling indignant with Bob's attitude. She wanted to keep her promise to Bob to love him in good times and bad times. > Beth , after thinking about this , finally decided that her love for him is paramount , regardless of the indignation he had caused her, and also because she wanted to keep her promise to him to love him always in/ through bad or good times.

the part you asked to check, it looks correct