Tarps are a tie down issue out of the box, but they’re pretty easily modified. Not in a cut and sew kind of way, so much as a fold the ends, and grommet the edges together kind of way. If you can locate a suitably proportioned box, you can wrap around that, use tape to hold the shape, binder clips to pinch the edges, and then put grommets in. (Grommeting kits are Cheap.) Then BAM! Bicycle cover!

Or, you could swing the other way and propose something like this: https://www.theparkcatalog.com/doubleup-double-sided-free-standing-vertical-bike-rack

I’m sure facilities won’t like being approached initially, but my experience with most folks like you describe are much happier when they’re not asked to do the creative heavy lifting. “We have this issue, I was wondering if you could do this specific thing to fix it,” goes pretty far sometimes. If nothing else, it shields the Eeyores from worrying that their efforts to help will meet with criticism, because now it’s not their idea, and thus not really their fault when it’s not good enough.

Maybe even put a roof over it, or mount inside.

Otherwise… not knowing what you’re talking about in terms of footprint and ceiling height, I can’t propose much that is context specific. But there are also plenty of wall racks, hoisting options, and so on…