I'm currently using two regular bags -- one to hold my meat and fish and the other to hold my vegetables and tailoring bolts. I have a Lure Master Tackle Box from my engineer just sitting in my bags because I don't ever have 32 stacks of fish at once to hold, and it hadn't let me hold cooking mats as I'd hoped.
But never fear, patch 5.1 will be here! Datamining at MMO-Champion shows three "Cooking Bags," which presumably will hold meat, fish, vegetables, special ingredients like 100 Year Soy Sauce, as well as the cooked foods themselves such as feasts. The smallest size is a 28 slot, aptly named a "Portable Refridgerator," and will be buyable from Nam Ironpaw for 10 Ironpaw Tokens. You can upgrade this bag to 32 slots and 36 slots via an engineer's craft. All bags appear to be bind on equip, and therefore tradeable.
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