Last summer, I carried a bear canister on that section of the TransAm:
http://www.rei.com/product/768901/bearvault-bv450-solo-food-containerIt fit nicely inside one of my Ortlieb BikePacker Plus rear panniers.
It is my understanding that hanging your food no longer works; bears have learned all kinds of ways to get it down. The only approved storage method in US National Parks(?) is a bear canister like above, which you just set on the ground. Supposedly there is one bear on the East coast that figured out how to open it. I found it hard to open--even after reading about the "trick" to open it--so I think it is quite a feat for a bear to have figured it out.
But for a cyclist, it is not the worse thing in the world to lose your food to a bear. There is usually a town nearby where you can resupply. However, if your pannier gets ripped apart that is much more bothersome. I discovered that all the hiker/biker campgrounds in bear territory along the TA had bear boxes. A bear box is a metal box next to your campsite which you can store food in. Bears know they can't get into them. Bear boxes aren't huge, and you have to share them with other campers, so it's not like you can put all four panniers in them.
The only reason you would need a bear canister is if you have to stealth camp, which I did once. I put my bear canister 100 yards from my tent, and I hung one pannier nearby the canister. I thought I would stealth camp more, but it is a real pain in bear country. In fact, I even stopped cooking entirely at the campgrounds--it was just too time consuming. Instead, I bought sandwich meat, bagels, turkey jerky, milk, nuts, fruit, carrots, and cookies to eat for dinner and the next morning's breakfast.
I kept all the things with smells in one rear pannier: toiletries, food, cook set, sunscreen, and baby wipes. I did keep Cliff bars inside a plastic ziploc bag inside my handlebar bag, which I made certain not to forget about when camping. I dutifully transferred the plastic bag containing my Cliff bars along with my food pannier to a bear box when I arrived at a campground. At most campgrounds, you are not allowed to leave *anything* on picnic tables. You have to eat, and then clear the picnic table completely. Supposedly, anything left on a picnic table will draw bears into camp.
The news of the bear attack "in" Yellowstone last summer spread rapidly among the touring cyclists. I think it is fraudulent for the news services to now claim that the latest attack was the first death in Yellowstone since 1986. If someone gets killed by a bear 10 feet outside of Yellowstone, it is still "in" Yellowstone as far as the public is concerned. I met a French cyclist in Yellowstone, who flew into West Yellowstone, and he rented a bike to spend a week sightseeing in Yellowstone, and he saw 5 bears. One bear ran across the road in front of him.
I suggest you read a book on bear attacks. It will frighten you, but it will also teach you some things you can do.