You can keep picking up Sweet Berries from the bush even after the bush has no berries at all. You can press the Use Item/Place Block button on it and keep taking berries, also when the bush has no berries you can break it and the bush drops the Item. You can also make the bush grow after placement when you use the Sweet Berries on it.
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We're actually already tracking this issue at MCPE-41211, so we will resolve and link this ticket as a duplicate.
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