They're looking for an example of your writing. I've done many on other topics. Make sure the grammar, capitalization and punctuation are perfect. And it wouldn't hurt if you use paragraph structure and a coherent narrative.
Type your information into a separate Word (or similar) document first so that you can Spellcheck and Grammarcheck it, making any need corrections. Then, save it somewhere that you can easily find it and copy and paste it into your applications as needed instead of having to retype it multiple times.
When writing a bio for mystery shopping think about the skills they would want--reliability, good observation skills, ability to self manage your schedule and obligations, good communication skills, good technical skills with the computer, camera, scanner etc. The ideal shopper is the one they can hand a job to and get it back, complete, correct, within the deadline and needing little if any editing. That is the shopper they want as it requires the minimal administrative time to handle (and time is money). So if you focus on your background and experience in a way that draws a picture of your competence in a grammatically correct narrative, what is not to love? And of course if you have a special background in retail or banking or some other area that is likely to be shopped by them, let them know about those skills.