In a query, you're writing personally to the agent or editor so writing about yourself should be in 1st person. But a bio is for the website, so 3rd is more appropriate. You can still be personal or have a cheeky voice, what you want to convey. For example, for an Odyssey article on DNP and weight loss, I wrote: VKB harbored tapeworms as a child in India. She remembers eating a lot and losing weight during those infections. Perhaps chocolate-covered tapeworms could be the next new diet fad. (Just kidding!) In her work as a microbiologist, she used DNP to study metabolism in E. coli bacteria. They all died as a result.
Good luck!