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Sample rate conversion math creates large bit depths that need to be reduced in order to store the audio as a standard computer file. Dither makes the bit reduction sound like noise rather than like distortion. Dither is not just noise that covers up the distortion so you need to dither every time you reduce bit depth in order to avoid distortion.
The least damaging way to do this is by taking a 24, 32 or 64 bit file, converting the sample rate and then reducing the number of bits to your target bit-depth using dither. This can all be done in one step or the conversion and final reduction can be done separately by making a 24/32/64 bit intermediate file when your sample rate converter's bit reduction doesn't sound as good as that of your other audio applications.
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