Up+A when the ball opens has worked for me ever since RBY...
In the Safari Zone, you have two choices: launch Balls until you get it (Works most of the time, and gives you enough tries if lucky.). The other option is throw Rocks, hope for it to stay, and then throw Balls. It's almost impossible to pull it off with the likes of Chansey and Tauros, but it's a sure catch. 2 Rocks dramatically heighten your chance, and 3 is a totally ensured catch (Most of the time...).
Unless it has changed in FR/LG (Unlikely.), Bait just makes the Pokémon less likely to flee, but makes'em WAY harder to catch... I stay away from Bait every time.