If you need to go outside airport you must pay $5 Brunei for visa. Taxi into town will cost $20 -25. There is some transport from across car park in airport - sort of dark blue-ish purple bus which is very inexpensive.Not sure about the timetable. Ask on Lonely Planet forum. We stayed at Radisson 'cos it had a pool and was a 15 minute walk to everything except the museums.
Singapore and Brunei dollars are used interchangeably in Brunei but all coins are in Brunei coinage. From memory the Brunei hotel is reasonable and has the bus station just behind it and so getting back to airport is easy. Bruneians speak English so it is easy to find your way around. It is very small. There is a market across road from Brunei Hotel. I read the hotel has been refurbished. I would stay there if I had a short stop over.
Alternatively you can opt to stay at the accommodation on airside. It is nothing flash but adequate and has only a double bed and en -suite shower and toilet to each room. Think availability is on first come first served. Google it as have seen photos of it. The SC rooms aredownstairs and I spoke to the concierge, or more realistically, the bloke in charge, and I think he said it was available in 6 hour blocks depending on demand.
I wanted to leave my luggage behind but was told there was no left luggage facilities. RB is building a new airport which I am sure will be fantastic.