Last I checked, you can't create more bits more often from whatever source you have. Best suggestion is better playback equipment. If that means you hear too much of the nastiness, many less capable playback equipment. In other words, play around more with what you have and see how far you get, or get better sources to see if that helps.
FWIW, I can certainly tell the difference between a CD and a LAME ripped version of the same song from that CD, and CD's aren't known for their sonic reputation.