eps files (along with pdf, psd, ai, cdr, etc) can contain vector and raster information. You can tell what a specific element is by zooming way in on it. Once you get zoomed in this is what you may see:
A vector element will remain a series of lines and curves at ANY zoom level. A raster/bitmap element may look like curves and lines while zoomed out but when zoomed in you'll see it's a bunch of dots of various colors.
I do some printing of art that should ideally be vector with bitmap source material. A good guideline for inkjet output is to make it at least 300dpi at full size, 200dpi is often "good enough".
Hmmm, sounds like your refinisher is likely using a cutter/plotter to cut masking stencils. There's a good chance that the cutter/plotter can do absolutely nothing with a bitmap file. (EDIT: Doh! Surely he's cutting vinyl decals to be applied. I've been watching too many of those hot rod shows)
To prepare a file for the cutter, you can trace the bitmap in Inkscape. You use the pen tool. I usually start by putting a node (by clicking with the pen tool) at the apex of each curve, at each corner and at the end of each straight line. Then I select all nodes, convert to curves. Then set about adjusting all the handles so that the curves look right. For your example decal, as mentioned above you can match the font. Many fonts will have to be hand traced, however.
Your first one will probably take a LONG time, but it gets faster as you get better.