Lots of places where errors can creep in with your process, not saying that is the case here but a few pictures or screenshots would help a lot as others have said. The best way would probably be to draw them using the vector tools within the software which unfortunately if you are not proficient can take time
You can use your scanned bitmap as a guide which may help.
What resolution are you scanning at & what file format are you saving the scanned image as?
I suspect the issue is that the OP is getting far too many nodes in their vectors from using the Trace Bitmap method.
As Martin said above, it would be beneficial to learn/use the vector creation tools in VCarve since you have FAR more control over the nodes. I have learned the hard way that there isn't an automagic way to create vectors from an image (I have tried other software, such as Illustrator (LiveTrace) and GraphicTracer, which work, for a "quick and dirty" method, but these programs also create (on average) far too many nodes, and if you are trying to do straight lines or smooth curves, you will likely always be unsatisfied with the results.
It takes time (especially the different type of curves, and types of nodes) but once you are proficient at it (learn the keyboard shortcuts!!!!) you will have complete control over your paths.
Another tip: if you are scanning the images, and there isn't a scale on the picture (unlikely, but you never know), place a ruler beside the template (when you scan it) so you can ensure the scale of your design is correct.
Tip#2: Make it easier to use your scanned image to manually trace your paths by right-clicking on the bitmap image and selecting Object Properties and move the slider bar to adjust the amount of fading there is on the background object (i.e the picture you are tracing, particularly if it is very dark).