We had a very nice stay in Kate's apartment. Kate was the perfect host: friendly, welcoming, and flexible in terms of arrival and departure times. The kitchen and bathroom are not big, but we were four adults and that didn't bother us. We had everything we needed for our short stay in Copenhagen.
There is a bus connection, which we found very useful as it stops only 100m from the apartment, departs every 5-10 minutes (even late at night), and takes you in just 10-15 minutes to the city center/metro/train.