To start, here are the basic mechanics:
What a coating does to a bow is simple: it converts the element of the attack to the associated coating. As far as I can tell, coatings convert the shot entirely to the coating's element, so a 300 Thunder bow with Poison coatings would be 300 Poison until the coatings ran out or were removed. By using the Poisoncoat jewel, all you've done is allow the Poison coating to be used, as some bows do not allow it.
When not using the coating on a non-Poison bow, the Poison Attack skill will do nothing at all. When using the coating, the bow will function exactly like a regular Poison bow.
With that information, it's easy to see what the Poison Attack skill will do.
- Level 1: Poison buildup +5%. Bonus: +10.
- Level 2: Poison buildup +10%. Bonus: +10.
- Level 3: Poison buildup +20%. Bonus: +10.
The skills will work just like they say. Add 5/10/20%, then +10. So long as you don't hit the cap for the bow, anyways.
To see if you hit the cap, though, there's a simple process: equip the bow, and preview armor pieces that add that elemental attack. Does the attack go up? Not at the cap. Preview another piece. Attack doesn't go up? You're at the weapon's cap.
When converting your element, however, this process is a bit more involved, as the cap may or may not be the same for the converted element as for the original. Best you can do for that is enter a hunt with +1/2/3 Poison Attack, equip the coating, and see how it affects the stats.