Please, please, please don't put your BPs on pine bedding. Oils and dust from pine can cause your BPs issues. Not sure about the other species since BPs are all I keep, but avoid using pine with them.
Back on topic:
I use pine shavings from my local Co-Op that's been finely screened for dust, and it seems to work very well. I don't have many, if any, dust issues. And I clean twice per week, and hardly ever notice a smell from my rats. Once in a while, if I've gotten a few too many rats in one tub and haven't yet gotten the chance to kill off and freeze some, you can kinda notice a smell; not sure if this is the case for you (the OP), but it's the only time I've noticed a smell personally. I usually kill off and freeze when I begin to notice a smell on my cleaning schedule, as twice a week is efficient at controlling smell for me as long as I don't overload the tubs. Plus you can have issues with overloaded tubs (rats may think they are overcrowded and could begin killing off any they see as smaller or "weaker") aside from the smell.