Unless the times or frequency changed, it would leave the hotel at 00 and 30 of every hour, it take about 12-15 minutes to get to the various terminals. It would leave the bus shuttle center at O'hare at 15 and 45 of every hour. It always left promptly from the hotel but I did experience once where the bus simply never came from the shuttle center and I had to wait an additional 30+ minutes on top of the time I had already waited for the previous bus.
Yes they provide shuttle
Yes shuttle is provided and leaves the hotel every 30mins.
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