I ran into this glitch last night, and again this morning after I loaded an earlier save to get back the rag, which the walkthrough I was following said was a required item to complete the bridge section. What I found was that having all of the items required, and more in one case, did not actually give me a better chance at completing the bridge section. I did eventually take a different approach, which lead me to successfully cross the bridge. Some of the things I was reading online about passing the bridge section stated that it was possible to pass the bridge section without having all of the items stated as required in the walkthroughs, which lead me to the theory that the bridge was only counting on me throwing everything I had in my inventory, regardless of the amount.
*SPOILERS BELOW*
To get around the glitch, I actually tried to minimize my inventory by using up items that would respawn themselves after each use, but not after being thrown into the bridge. The rag that I had previously brought back with me from an earlier save, I decided to use it to shine the metal thing, which removed it from my inventory. I also used up the hay and carrots in my inventory. I did not try to use up my zorkmids, which I think I could have done, and then replenished from the tree, but lucky for me I didn't have to. I started the process of throwing my minimized inventory into the bridge until I had nothing left. I found that I got very close to raising the bridge, about the same spot that I did with the maximized inventory, so I headed out to get the extra carrots and hay. I noticed that another steak had spawned at some point in the refrigerator, but I decided not to grab it unless this next attempt was not successful. I warped back to the bridge, threw the hay and carrots into the bridge, and was happy to see that the bridge was finally safe to cross.
One additional thing that I did, that I don't think really made a difference, was to go into the inn and stay for a night, which I had skipped completely due to the walkthrough leaving that part out. I got some extra points and a nightmare dream sequence to watch, which made it worth it enough, but it should be noted that there were no additional items to pick up there.