The bait bag is available for purchase right from the beginning of the game on Outset Island. You may not have enough money to buy this right from the beginning of the game, but once you do, head back to Outset island to get the bait bag.
When you are on Outset island look out to the sea, you will see a boat sailing around the water, very close to the coast. Sail or swim out to this boat and go inside.
Inside this boat, you will see a store. There is an item for sale that looks like a pig head, this is the bait bag. Once you purchase the bait bag you will also be able to purchase bait to put inside the bag. This will allow you to talk to the fish and add map information to your sea chart.