I think this is how it must work:
-bottle is full of water
-Herbert blows into the bottle through the straw, thereby trapping air in the straw and at the top of the bottle (an air bubble).
-the water in the bottom is of course at the same pressure as the water outside the bottle.
-as he descends the air in the straw and bottle compresses, and the bubble appears to retreat up into the straw somewhat as he descends, but there is enough air for him to use when he needs it.
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