This isn't a main plot point of the story, as I envision it now, it is just an example of her inner fantasy life. I need for X to be some creature or being that is known for not wanting to be around humans--for wanting to hide, to be left alone, or to run away from humans. Ruling out all creatures or beings that seek to play tricks on, seduce, or kill humans.
My mind went immediately to unicorns as being solitary and wanting to be left alone, but unicorns are kinda overdone, and then there's that "taming by virgin" motif, which doesn't fit. I'd rather use something unusual that my character would discover in a book, not something like a unicorn that she would have always known about.
I also thought of the Yeti or Sasquatch, but I really doubt she would want to imagine she was a Yeti. If there's a similar creature that isn't so strongly known as male, giant, and hairy, it might work.
My character's mother is a librarian and she is a prolific reader of fantasy even in her most locked-in periods, and she's also a big computer user, so this being could be from any mythology; it doesn't have to be something that is common knowledge to people in the northeastern United States, where the story takes place.
The creature/being could possibly be one that is comfortable among its own kind, or one that is solitary. It can be partially or even mostly unpleasant (she's certainly got some self-loathing), but there should be something about it that makes it attractive, so that daydreaming about it is a soothing thing.
Since my character is currently sleeping during the day and waking at night in order to minimize interacting with her family, a being associated with night would be ideal, but please offer any suggestions you have.
Before people ask: no, I'm not planning on having her be otherkin.
I've found Googling difficult because I can't use "myth" because it's so often used to mean "misconception" (such as "top ten myths about shy children"). Here are some example search terms: shy "mythological" creature, shy myths, shy "mythological" beings, reclusive "mythological" beings, "mythology" "afraid of humans"
I also browsed around on Wikipedia for a while by looking around their various mythology categories, but they seem to have everything categorized by culture ("English legendary creatures" etc), and since I don't care where it's from, that makes looking through the many stubs very onerous indeed.
My "mythology" "afraid of humans" search gave me the ciguapa which looked promising but further searching informed me that the "afraid of humans" bit was made up for that particular children's book--the original myths about ciguapa have them luring men into sex and then killing them, similar to sirens.