you can get more potion bottles from quests but that is very rare.i am at level 34 (myth) and i only have three potion bottles. so don't expect to get a potion with every quest.
No potion bottles are given with quests. You get one when you finish Unicorn Way and talk to Merle Ambrose, one when unlock Krokotopia and talk to Sergeant Major Talbot, and one when you unlock Marleybone and talk to a character there.
