Because the Empire Hotel & Country Club is located at an exclusive area of Brunei, the best way to get there from the airport is by taxi. Luckily the hotel is not far away from the airport, and the taxi journey should cost you around $20 brunei dollars one way.
There are some taxis outside the arrival hall of the airport, and the airport is not very big and crowded so it is quite easy to find. There should be no safety concerns as Brunei is a very safe and wealthy country.
As the Empire Hotel & Country Club is very big and the buildings are spread over a large space, a good way to move around are by the buggies (see photos) provided by the hotel to its guest free of charge. The staff drivers will send you to your destination, and if you want a buggy but none are available, simply contact the hotel via telephones at the various pick-up and drop-off points of the buggies.
If you like exercise and want to take photographs, the best way to explore the various areas of Empire Hotel & Country Club is by walking. Being a top-range hotel, the paths are easy to walk with lots of signages. You can even obtain a map of the hotel and its surroundings from the check-in counter when you arrive at the hotel.
Personally, I really enjoyed walking around the hotel, experience the pleasant surroundings and took lots of photographs :)