Like you, I had found that census for Rebecca in Bibb County. However, if you continue to trace the family to 1880, you will find that Rebecca  was married to a Smitherman and had several children. In 1880, her parents Daniel  and Catherine  are living with the Smitherman family. I thought sure that I had found her and was disappointed to find out that she could not be your Rebecca.
Sorry to give you the bad news.