One extra halter/lead between the two of you is plenty if you both have regular halters plus a show halter--because a show halter will work just fine if you lose/break the rest.
When we go to shows, we put the hay bale in a garbage bag. It works just as well and it's easy clean up. It also works to line the floor underneath the bale if we have to set it on the ground outside the stall, and it's easy to put loose hay back in it.
Bring a chain or something to secure the water bucket. If it has a handle, it doesn't need to be left on the ground. Haystrings work well as cheap ties ;).
Have all of your grooming/wash stuff (brushes, clippers, shampoo, sponge, wash bucket, fly spray, combs, show sheen, etc.). You might want to invest in a hose, or make sure someone from the barn has one. Not all wash facilities come with one, and occasionally they are broken, missing, have holes in them, etc. You might also want to bring a sprayer attachment for the end of the hose. Bring a box fan for your horse and brings ties (again, haystrings work!) to secure it to the stall. I suggest bringing an extension cord and a multiplug strip as well because there are never enough outlets in the barn. Use either plastic zipties or electrical tape to secure any electrical cords to the tops of the stalls so they don't hang loose and get chewed on by a horse. Bring a sign for the stall door that has your name, barn name, and contact info in case of an emergency. Bring something to secure the stall with if there is any doubt about the suitability of the latch (our 4-H barns have horrible latches and we always put a halter or chain around it as well, just in case). If you get a tack stall, bring a lock. I like having a tack hook/hanger to put bridles, halters, etc. on when I'm rushing around getting ready.