1 - Level of Opponent - As far as I can tell, the higher the level the opponent, the more BP you can earn off of them.
2 - Strength of Defense - Beating a harder defense earns more BP.
3 - Strength of Offense - This one is the most noticeable variation for BP earned. The higher your ATK total after skills (Cannons, other modifiers), the more BP you earn. You can increase your BP with a really good Assist.
4 - Number of Wins - Don't aim for a 3-2 victory, a 4-1 or 5-0 victory earns you more.
5 - Letter of Marque - Obviously, be a part of the losing Nations.
6 - Guild Brawl - Multiplier for your BP total.