Just read that Agatha Christie wrote her first novel on a dare from her sister, found that in a biography at my local library. | Creative Writing Prompts - Talk Freely
But what if the bet story is just a cover? Maybe she was tired of people asking where she got her ideas and made up a simple answer that sounded better than "I was thinking about poison while sorting the mail.
The biography I read said it was a ten shilling bet with her sister Madge. That's a specific amount of money for the time, not just a vague story. Writers often give a tidy answer because the real process is messy and hard to explain. I'd trust the documented bet over a later rumor.