Bunnies, especially teenaged ones, do tend to mark beds at some point, and it sounds like she’s comfortable and both marking and doing her thing without bothering to get off to find the litter box. You need to stop allowing her to do this. I would suggest either not letting her on the bed, or
put a second litter pan near the bed in the room. When you see her wiggle her back end or lift her tail, scoop her up as quickly as you can and place her in the litter pan. Praise her once she’s in there, and if she goes in the pan, give her a small treat and praise. (Like a raisin.) If she goes on the bed, say No firmly, put her in the litter pan and use a paper towel to soak up the pee and set it in the pan with her. Then pet her in the litter pan.

You are using positive reinforcement to teach her to go in a litter pan instead of anywhere else. Punishment doesn’t work, but training can work quickly. She will learn that there’s a payoff to NOT going on the bed and choosing a litter pan instead.

You could be seeing the calcium sediment they excrete in their pee. It can be more noticeable when they pee on fabric or other absorbant things & the moisture is wicked away.
If its more like mucous then that would need vet attention.

My foster rabbit does drop cecal pellets also when he’s marking. He’s the only one I’ve seen do it.
They do coat regular poo with a substance when doing territorial marking. It has a bit of a sheen & smell. (lovely!)