Here's the method I use
when you fish, look closely, when "Oh! A bite!" flashes in your text box (it will always be under the line of dots) press A once. the text box will clear, and another line of dots will start to form. After a while (its a different amount of dots each time, you just have to pay attention) "Oh! A bite!" Will flash again under the line of dots. Once again, press A once. The process will keep repeating until it tells you that there is a Pok?mon on the hook.
Note: If you press A before "Oh! A bite!" appears under the line of dots, you will lose your catch ("It got away...")