plastic storage containers or large plastic rubbish bins can be used instead of small buckets. Just make sure they haven't had any chemicals or cleaning products in.
I would just rinse it off under the tap. I've never "soaked" any wood, and my tanks are full of chunks of wood and branches. You would basically need an empty tank of water to soak this, but it would not achieve much. The tannins are not going to be much.
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I don't think my mum will be happy if she sees a bath full of water with a piece of wood soaking in it . I might still look into soaking it mainly because I'm going on holiday next week so might be worth leaving it soaking for a week. I've never kept wood so don't know how it would be. The wood actually arrived yesterday so might look for a container in the garage to soak it in. Most importantly properly clean it.
Never soak any aquarium wood or rock in a sink or bathtub. There may likely be chemical and soap residue (no matter how well rinsed) that if present will get soaked into the wood. Toxins like these can leech out months later.
Same holds for any container; unless it is only for (and has only ever been used for) aquarium/fish things.