For all those coming to Copenhagen for ICANN 58 Hotel Bella Sky does have 
an airport shuttle and the cost is included in your room rate. Per an 
e-mail received today from the hotel:
  
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 The shuttle operates daily between 06:30-22:30 on a first come first 
served basis.
Frequency is every 30 min and departure is from outside terminal 2 at the 
bus stops.
Pre order from the airport to the hotel is not possible. However, from the 
hotel to the airport you have to make a booking at the front desk.
 
The shuttle costs DKK 15 but this is included in the room rate.
 
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 I hope this is helpful.
  
 Safe travels everyone!
  
 Ed Morris