var earliestCheckInDate = items.Min(x => x.CheckInDate());
        var daysToSubtract = (newStartDate - earliestCheckInDate).Days;

        foreach (var item in items)
        {
            var incorrectCheckInDate = item.CheckInDate();
            var incorrectCheckOutDate = item.CheckOutDate();

            item.SetCheckInDate(incorrectCheckInDate.AddDays(daysToSubtract));
            item.SetCheckOutDate(incorrectCheckOutDate.AddDays(daysToSubtract));
        }

var items = booking.ActiveItems(); // each item has check-in and/or check-out dates

var offset = items[0].GetCheckInDate().Date - DateTime.Parse("2017-05-12");

foreach(var item in items)
{
   item.SetCheckInDate(item.GetCheckInDate() - offset);
   item.SetCheckOutDate(item.GetCheckOutDate() - offset);
}