Really? Is this feature present in all the games, or just 3G? I'm playing P3rd and I have only 3 inventory pages + quest pouch when on hunting.
Anyway, I'm a new hunter myself and maining bow right now. But I also have a cople of advices to give. There's a limit to how much coating of one type you can take with you on a quest, but you can have as many coating types as your bow supports. And don't forget that you can mix coatings right in the field, but the amount of ingridients and empty bottles you can take is also limited, but it's better than running out of coating early.
My bow has only lvl2 pierce shots, but if lined up properly it can do up to 4 hits even to a monster size of Great Jaggi. But yeah, pierce is obviously more effective the longer your target is. One little problem is that you have to stand right in front of a monster to make the most of the piercing effect (or right behind it, but they rarely give you a chance).