What makes you reasonably certain it's not a protective plate? I ask because this is almost by definition what a protective plate does.
This is likely protecting an electrical cable. When you run wires to outlets or switches, it's good practice (and required by code in many places) that you place protective plates on the wooden studs where electrical cable has been ran through it. This is an important safety measure, to keep you from drilling or nailing into a live electrical cable.
for example:
Quick version: You have metal studs. Install tips below.
Long version: This is a good question with a lot of detailed information; kudos. Perhaps I am missing something, but the information provided leads to a clear conclusion IMHO. A building that tall built in the 90s in the US will have metal studs (99%+ chance?), so what you're finding matches expectations.
To be safe, go ahead and use that stud finder or your knuckle to confirm you have 16" OC (on-center) studs all the way across the wall that line up with the original 3. If so, then it's pretty clear... metal studs, you have!
If you want to be really safe, or just cover your butt, ask the building super or maintenance person to stop by sometime. A building that big almost certainly has someone who stops by daily or is maybe full-time; just find a time to say "hey, I'll be home 3-6pm today... could you stop by when you have a sec?" They're usually happy to help. Ask if they know the building has metal studs, and it wouldn't hurt to ask their advice for install. If something goes horribly wrong later, at least you asked the pros.
Next, yes, use toggle bolts. 5/8" drywall and metal studs aren't designed to hold much weight, so use one toggle for every 50-100 pounds of weight to be safe. There are lots of posts on this site about doing that, but here's a good one: If my wall has metal studs, is it better to anchor heavy objects through just drywall or also through the studs?
Depending on how your bed is designed, a plywood backer board might be wise, e.g. Can metal studs support a 64" plasma TV on a swiveling mount? Most likely, I think, this will be unnecessary because your bed will already be designed to spread the load evenly across the wall. Post pictures (perhaps in another question) if you aren't sure.
Finally, keep in mind that the load you're attaching will be moving a lot, unlike a TV or even a bookcase, so make sure the bolts are snug and don't allow the back of the bed to jiggle at all; err on the side of caution and put a few more toggles in than the 200-360# limit suggests in those links above. 1/2" holes are easy to patch and paint later.
Best Answer
Stop. You probably hit a metal plate protecting plumbing or wiring behind it. It's there specifically to prevent people like you from drilling through it and electrocuting yourself or causing a flood.
I recommend you stop whatever job you're doing and consult a professional, or at least a handyman.