There are a few WR bags you can try to get, but you need ones that are at least LARGE to carry ore. I'll mention some here.
Giant Burlap Sack, 10 slot GIANT with 40% WR, dropped by Burnog the Poor, a hill giant in OSM. You can solo this.
Cleric's Traveling Pouch, 6 slot LARGE with 55% WR, dropped by a wandering cleric in the Tiger's Roar in King's Pass. You can also solo this if you're careful.
Seeker Apprentice Satchel, 8 slot LARGE with 35% WR, gotten through the quest for Seeker Herina when you get far enough in the Main Quest. It can be upgraded to...
Seeker Storage Satchel, 8 slot GIANT with 50% WR, after turning in enough cores to Gavin (when you get far enough). Must have the above one to get this.
Supplier's Satchel, 8 slot GIANT with 35% WR, from a liodreth supplier in Paw above the room with the tamed lions. You should be able to do this, but it might be tough.
In addition, there are some other purchasable options if you don't mind spending the plat for them. It would help to keep an eye out for people or groups in the areas where these drop, as they are not always kept to sell to players or even vendors.
Filthy Ration Satchel, 8 slot LARGE with 100% WR, from East Plaguelands.
Shadow-Woven Backpack, 10 slot GIANT with 50% WR, from Lasanth.
Finally, there is the option of getting a 34 or higher Magician to summon you some Summoned: Dimension Holes, which are weightless, 10 slot GIANT with 100% WR. The downside is that they become Exhausted Dimensional Holes if you log out with them in your inventory, making them really heavy and 0% WR. So if you do this, you'll want new ones summoned each time.
You can also buy Handmade Backpacks from tailors which are 10 slot GIANT with 20% WR, and they aren't lore. I use these for mostly everything, but I don't try to carry 1000 stone of ore on me.