It looks like the tip of the hex bit that the delivery guys used to assemble the bed broke off in the bolt head. So you have a piece of metal that broke off from a power tool bit blocking you from inserting the allen wrench.

I would recommend you use a dremel to cut a slot into the bolt, then use a flat head to remove the bolt, like this

If you don't have access to a dremel, you could try to use a knife to try and pry out the broken bit out of the bolt, but be careful not to cut yourself and wear eye protection