Me thinks bonus shots are random and that the number of bullets that hit the enemy increase the ring size, i could be wrong tho. As for when to hit, i usually go for right it after the enemy bounces from the ground once.
Shots fired (ones that actually land) increase the chance of a bonus shot. If you stay on the ground, and bombard an enemy with shots, the chance of it occurring increases.
As for when to shoot, it depends on what you are trying to accomplish. To do ridiculous amounts of scratch damage, use machine guns. To have a better chance of shattering the enemy's hp gauge, handguns.
In either case, wait until the enemy is about to hit the ground. As soon as they slightly bounce, fire. For large enemies, fire as soon as they hit the ground.
All these things lost, like tears in the rain. -No matter what god you follow, they all seem to enjoy ironic fates...-
Bonus shots have a set chance of occurring and the chance increases if you have a shooting star equipped. The size of the ring is based on the amount of hits you do. So, an MG user with increase the ring much faster.
With a shooting star once the enemy is airborne I almost always get a bonus shot within 3 shots.
"Playing Bayonetta feels like losing your virginity over and over every time you pick up the controller." ~ Echo738
I'm pretty sure that the chance to activate bonus chance is fixed. I feel that my bonus shot activation is around one out of three times regardless whether I have 0, 1, or 2 shooting stars equipped.
So what does Shooting Star do? It increases the amount of yellow you gain for each shot you hit the enemy while they're airborne (ie. the part of the ring you have to hit to get the actual bonus shot)). It roughly doubles the amount of yellow you get for each shot hit an airborne enemy. This gets really noticeable once you get 2 shooting stars, as you can easily get a bit less than half of the ring already covered in yellow with just one attack of 25 bullets in a hero action (assuming the first bullet lifts them up).
Turn 1: Enhance Spells Turn 2: Overdrive, Water Blast X5