Bonus health means health gained from items / runes / masteries.
At level 18, Shen naturally has 1958 health*, so Ki strike bonus damage is equal to (Total Health - 1958)*.08.
*Shen suffers from a reduction in health due to the Inverse Ninja Law when Akali, Kennen, or both are on his team. This will reduce the base health of all involved by 1 or 2, giving Shen a range of base health from 1956-1958.
First, let's clear up a misconception.
Armor Penetration gives you a constant %damage bonus, regardless of how much armor the enemy has see here.
It doesn't matter if your enemy has 300 armor or 15 -- penetrating 10 of that will have the same effect on total DPS increase.
That said, let's take a look at why Armor Penetration is preferred, even with its linearity.
Attack Speed is easy to acquire via items.
Armor Penetration is not.
You can more than match the effects of attack speed runes with a single dagger - 420 gold.
The cheapest item with Armor Penetration is the Brutalizer at 1337 total gold. By this metric alone, Armor penetration runes are worth approximately three times that of attack speed runes.
It is easier to use items to stack Attack Speed over Armor Penetration -- but to get the highest DPS, you want to stack both.
Given that the amount of Armor Penetration available via items is strictly limited, if one's goal is to achieve maximal values for both Armor Penetration and Attack Speed, runes for Armor Penetration are much better than that of Attack Speed.
Best Answer
Different skills have different AD and AP scaling. For example master Yi's alpha strike increases in power equal to 100% of your AP. So building AP would increase that skill. However, Garen on the other hand has his skills increased by attack damage. So it depends on what champion you are playing and what how you want to play them. Just note that Ability Power does not increase the power of every ability so you need to know which ones do and don't. Master Yi is a champion that I've seen been used AP and AD.