Firstly I'll thank @John Cavan for providing the link to the Bichon Frise Club of America.
My mother and grandmother owned Papillons for many years. Papillons have lone fine coats and require very regular coat care.
We (as our pets have always been a collective ownership :) used an assortment of implements to groom the dogs. A variety of brushes and combs. It was interesting and reassuring to see the Bichon Frise Club of America also recommend this.
Metal and plastic combs (designed for humans) can both be useful in dealing with difficult knots.
When the dog is not maintained daily:
Firstly, using a brush, I'd suggest a slicker brush to begin with to remove smaller entanglements, then a pin brush. Some pin brushes have more spaced pins than others, I would recommend one with decent spacing, as opposed to close spacing, as it acts like a comb and a brush and will help untangle knots a brush cannot.
This then leaves the more difficult knots and is where a comb is handy. Working on each individual area with a comb can be effective in removing knots. Sometimes it may required careful snipping out matted fur that is beyond successful grooming.
When your dog is maintained daily (which is optimal for a Bichon Frise) you can lightly brush through the dog, but keep the focus on using the comb. There is nothing nicer than combing through fine, untangled dog fur.
There are also an assortment of detangling techniques that can be used in conjunction with brushing, especially combing.
This answer provides some good advice about dealing with the differing fur types on your dog.
If you go here, you'll find pictures of all the recommended tool.