Ways to obtain bags

There are a few quests that'll give you bags: http://www.arcgames.com/en/forums/neverwinter#/discussion/517007/bag-quests but they're neither particularly large nor particularly abundant.

Apart from that, the only ways to get bags are either through the Zen Store or the Auction House.

Also, take note the Bag of Holes that you can purchase is a 'gag' item and doesn't allow you to store even a single item in it.

The last (3rd) bag you get from a quest is in Neverdeath. It comes from Chettlebell and involves doing the clock dungeon place. In order for that quest chain to pop up, though, you have to do the quest from the Doomguide that involves killing Bone Porters. After that, new quests will show up with Chettlebell and Harper Windle.

Good luck.

You can buy bags in the Auction House (AH), but they are so expensive no one can afford them early in the game.