Let's look at a champion with 50 AD that owns a long sword. That long sword gives 10 AD, which makes their new total AD 60. If they were using an ability that scales 100% Total AD, that ability would do it's base damage plus 60 damage (100% of the total AD).
If it scales 100% bonus AD, then it would deal the combined damage of all of the sources that gives you AD (Runes, masteries, items, buffs), but NOT counting your base AD (What you have WITHOUT runes, masteries, items, buffs). In this case, if we look at it in a vacuum with just the long sword, the ability would deal it's base damage, plus 10 damage (100% of your bonus AD, which in this case, is the 10 AD from long sword)
Therefore, if you have 50 base AD and an ability scales with 20% of your base AD, the final scaling would be 10 ( 20% of 50)