I don’t think this is a bug. You get that badge for having a bio and profile picture, not for writing and deleting a bio. We wouldn’t want you to game the system, would we. 
This badge is granted for filling out your user profile and selecting a profile picture. Letting the community know a bit more about who you are and what you’re interested in makes for a better, more connected community.
When you remove those things, you lose the badge and it will be granted again as soon as the requirements are fulfilled.