There are 3 free bags that you receive before level 30 from questing.
18 Slot Bag – Finish the Blacklack District quest line
12 Slot Bag – Finish the Neverdeath Graveyard quest line
12 Slot Bag – Finish the Benign Order of the Third Eye Campaign
Alternatively, you can purchase bags from the Auction House with 12, 24, or 36 slots! Warning, this is expensive.
Cheaper, but more time consuming, you can run the Rise of Tiamat Epic Trial in hopes of receiving a 24 slot bag. Warning, low drop rate.