In order to use the fish bait, first ensure you have unlocked the fishing quests with the Mayor and Ricardo the fisher. Once you have a fishing rod, you can either gather bait or purchase it from Ricardo with gold.
First click on the fishing rod near your intended fishing area, and then the bait menu will become available to select the bait you have.
Then select the correct bait for the desired fish. The fishing rod icon will now have bait shown in the upper left corner.