refrigerated dough rise time in humidity

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how long does an overnight refrigerated dough need to rise (approximately) in a humid container, before baking?

The bread is a loaf multigrain. The container is a styrofoam ice chest with a bowl of bowled water under the loaf pan.

I don't think it matters much as long as it's "long enough".  Much would depend on whether the dough got a chance to start rising at room temperature before going into retardation.  If the dough started to rise visibly before chilling, then it would take a few hours to mostly stop any more action.  Longer would mostly add to the flavor.

If the shaped dough went right into chilling after bulk ferment, you might need a few more hours, but not that much more since it would have been rising already.

I usually keep my loaves covered with plastic wrap so the humidity wouldn't matter.

TomP