Yes, a bowling ball will absorb water. When I first started using hot water baths for bowling balls I did a little experiment. Using my digital scale I weighed a ball before putting it in a bucket of water and leaving it for a couple of hours. I forget the specifics but there was an increase in weight after soaking. To get the water out just put it someplace where there is air circulating. I don't know how long it will take, but it will eventually equalize with the room humidity.
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Moon
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So many questions, so little time but I'm having fun.