Normally, bedskirts are fabricated with a flat piece that goes over the box spring, then the skirt hangs from the seam. You'll likely have to get something custom made. The problem, though, is the metal frame is actually inset from the edge of the adjustable platform, which would mean the bedskirt would hang "inside" the width of the mattress. It should align with the edge of the mattress. What I might consider is creating an upholstered frame that matches your headboard that the metal frame sits inside of. That would hide the metal legs.

I think I would velcro a skirt to the black frame.

I would attach the bed skirt....with pins or Velcro strips....to the gray cloth “box” that articulates. I would NOT do a gathered skirt. I would do one that is tailored and has pleats. Yes, when the bed moves, it will articulate. It might wrinkle, too, if you leave the bed in an “up” position. So I would recommend that you lower the bed during the times it is not in use.

I would think you could velcro a skirt to the gray edge. Since the mechanics are inset, I don't think it would get tangled.
But they make them for adjustable beds

Bedskirt for adjustable beds

olychick’s is the best answer!

My computer seems to be full of gremlins today. My most recent comment didn’t post. Originally, the decorator and I were going with linen for the bedskirt. I think now that we’ve finally seen the bed, she is going to look for a nice fabric with a little poly in it to minimize wrinkles. Seems like my best bet is going to be attaching the skirts to the gray part. I read where someone even suggested that at the bend, place a slit that looks like a pleat.

Is a bedspread out of the question?

No bedskirt.

Our adjustable bed base is different from yours. It is quite a bit thicker, and upholstered/padded, but with metal legs. You can attach a headboard and footboard to the base. We added our headboard but do not use the footboard as we have a largish chest at the foot of the bed. I do not like underneath the bed to show. I had a bedskirt custom made it's the flat pleats and attaches with velcro. Works great. As I mentioned in your previous thread, we do not adjust the foot of the bed, just the head.

Also, our bed is normally left flat, unless we are in it, so when the bed is not in use, it's made and the bedskirt looks normal. Honestly, I've not looked at the bedskirt while the head is up but adjusting the base doesn't pull the bedskirt out of place. Hope all that makes sense. LOL

Also, if you google, there are ready made bedskirts for adjustable beds.