Like you, mine changes with the publication.
For short stories, I try to keep my cover letters crazy short. My main goal is to create a positive expectation of me and get them to start reading my story.
If I have absolutely no experience with the editor I normally give one log line about the short story. Then, I give a couple bio sentences and that’s about it. If I can find something the editor has written, I like to comment on it (if they’re reading my story, I think it helps if I prove I read one of theirs.) Or I may make a comment about a story in their magazine (For example, I’m getting ready to submit a story to Esquire–fingers majorly crossed–and in my cover letter I mention that in their latest issue they said modern authors don’t know how to write about sex anymore. So I told them this submission is how I’d like to prove them wrong. It’s cocky, but I think it fits the magazine’s vibe, plus it proves I’m a reader.) I don’t do this if my comment about the magazine is just going to be something generic like: I loved such and such story.
If I’ve sold the editor something before, I remind them.
If it’s a magazine that claims they do not care about author bios, I don’t include one. Do you think that’s best?
That’s about all I can think of right now. I get way more rejections than acceptances, so I don’t know how effective I am. Plus, I’m still trying to build my bio. Like I said, fingers majorly crossed about the Esquire submission.