Yes, in your carrier you can put shavings and hay. When the animals are in the cages for an extended period of time, for example, driving out of state, I use hay cubes. Otherwise, alot of times they will lay the hay down as bedding and make a mess of themselves. But in your case, it should be fine to put loose hay in there or a hay cube.
Ryerson also sells show cage feeders. This is what most ranchers use at shows to feed. I should have some extra feeders at this show if you can't find any in the next week.
As far as water bottles go, Sumiko (aznmexaggie) sells the smaller travel bottles, which are perfect for show cages.
As soon as you get to the show, you can transfer your animal over to a show cage and get all set up. I would bring loose hay with you to give overnight.
See you next week!