There are five bottles that can be obtained in Link Between Worlds. This page explains how to get all five.

1. Buy one from the merchant in Kakariko Village who sits outside on the blue rug. It costs 100 rupees.
2. Get Zora's Flippers by going to Zora's Domain in northeast Hyrule, then going to Kakariko Village to buy the Shiny Stone from the outdoor merchant and returning it to the Zora Queen. Then swim under the bridge south of the Eastern Palace and talk to the Bird Lover to get the bottle.
3. East of the House of Gales, look for a bottle in the shallow water. Take it to the Milk Bar and show it to the owner. He replaces the letter with Premium Milk. Go talk to Rosso, who lives east of the northwest forest of Hyrule. He'll give you the Power Gloves. Go into the cave south of his house to reach Death Mountain. Go to the top of the mountain and go east. Use the Hookshot to cross the broken bridge. Go into Rosso's Ore Mine and go to the south exit. Outside, you find the injured boulderer. Give him the milk to get the bottle.
4. Put a bomb on the left side of the rear wall of the Vacant House in Lorule. Go inside and open the chest to get the bottle.
5. Go to the house just south of Thieves' Town, where you find the Bomb Flower guy. Ask to borrow the bomb flower, then check on the bomb flower to make it follow you. Put it behind the cracked stone south of the fenced-in area, then hit it to activate it. Run away before it explodes. Now get another bomb flower and put it in front of the crack northwest of the Bomb Flower Guy's house. Go into the cave that you reveal. Go up and stand on the rupee symbol, then keep throwing 200 rupees into the pond. After you throw in 3000 rupees, the Great Fairy gives you an empty bottle.