I took alot of time to get this right as well.
The moment you get a bite press A. If you delay for too long the Pokemon will flee and you lose your fishy ;-;
You'll have to do this several times in order to finally battle the Pokemon (It may be as short as just 1 time or maybe 5+ times) - complicated I know. Don't worry if you fail alot, it happens, Emerald fishing is really difficult.