Late last year, I went to Brunei for around 5 days. And K.H. Soon Resthouse is the cheapest accommodation you can get in BSB- well, still expensive for my standards as I am a super budget traveler. This room costs BN$39 for one night (which is around US$32), has its own toilet and bath. I almost gave up as almost all of the rooms have bitchy airconditioning, but last room I entered was good so I stayed in.
Personal TIP: You’re better off staying somewhere in the Gadong area. There’s not much to see in the capital Bandar Seri Begawan anyway and Gadong is livelier and more dining, shopping options. Realistically speaking though, Brunei is a very small country and 2 to 3 days will be enough already to see everything.
One downside is that public transportation options are very limited- if you do not have a local connection (which has access to a car obviously) and found yourself roaming in the evening, then you’re in trouble. The buses stop operation at 6PM and beyond that, you will need a private car (or cab if you are lucky to find one) to travel from here to there.
Generally though, Bruneians are very warm and friendly so when you get there, relax and enjoy every moment of your journey.