how is bitmap image converted to vector image in preparation for making silkscreen print?

Answer 1

There are programs that do it.
I downloaded the trial of Scan2CAD and used it to convert a picture of a car to a 2D vector file. I had to play with the image to sharpen the edges and increase contrast before I got a result with longer vectors and not a lot if itty bitty pieces.
Basically they take changes of color and tone to be edges and mark out the edges for vectors. With a more complicated program than the one I used (as I recall), you get the regions inside the vectors colored.

Answer 2

Several programs will translate a bitmap to vector including Corel Trace. It comes packaged with Corel Draw (a MUCH more user friendly program than Adobe Illustrator). You can set it to trace verbatum or abstractly and with textures. It takes a few practice times but you'll get the idea and flow with it.
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Answer 3

FlexiSign will trace your bitmap.

I have been in the sign industry for 13 years, when will people get that bitmaps are NOT artwork. One of my biggest gripes.

GOOD LUCK!