Just to add to what you have said Phil, if you are printing bitmaps & then scanning them there are other things you can often do which can help, most scanning software has filters that allow you to exclude some of the unwanted dots (or noise) that you often get with low quality images, you can also tippex out any parts of the image you don't want rather than scan & then try to remove
If you play about with the scanners filters these tippexed out bits can be completely removed.
Something else that people often make a mistake with is that they size the bitmap before they trace it, enlarging a bitmap reduces the resolution so you are always better to trace your bitmap at it's original size & then enlarge the vectors to the required size.
If you can then it is often best to make some changes to low resolution bitmaps before you import them for tracing, I use dedicated software that I have as a signmaker to increase the resolution of bitmaps but most photo editing software will contain filters that will do it, guessing even the free software will have some way to do it even if the results are a bit limited. There are a lot of other things that you can do using photo editing software which will help you achieve a better trace but that is a whole new subject on it's own