I'm using SmartPots and some big 32 gallon storage containers I bought at walmart for 7 bucks, just poked a bunch of holes in them with a wood burner. The smartpots are a spunbonded polypropylene fabric, much like the texture of a stiff felt, but wont rot or decompose, and are completely re-useable. Just wash them out and you're good to go again. The storage containers are big, cheap, and easy to find, just gotta poke drainage holes, though they are rather unweildy. Here's a link showing what I did.
https://www.rollitup.org/outdoor-growing/383815-diy-smartpots.html
The smartpots on the other hand, come in HUGE sizes, up to 200 gallons! And the 30 and 45 gallon ones are about 14.99-17.99 each from the website. They're flexible, breathe like crazy, and somewhere between a grow bag and a pot.
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As for worrying about buckets being too clumsy,
can you imagine anything being a bigger pain in the ass to move or manipulate than a garbage bag full of soil? There are a lot of creative solutions out there for people who can't plant in-ground. Just keep looking and I'm sure you'll find one that works for you.