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Either open your existing colored texture map or create one in Photoshop using paint tools. If you're just looking for a generic texture and not something specific like facial shading, you can use layer styles such as the Pattern Overlay to generate a repeating texture. For specifically painted detail, you'll need the exact map to make sure that the color-painted highlights and shadows line up with the bump map's texture extrusions.
Save a grayscale copy of the map. To turn a color version into a grayscale version, use the Desaturate function under the Image-->Adjustments menu. If you've generated your texture using layer styles and pattern overlays, you may need to flatten the layer so your adjustments affect the texture and not just the base color underneath.
Depending on the type of shading you've done, you may need to invert the image. In the original color version you'd have painted shadows dark, and more elevated areas would be brighter, more exposed to the lighting / tone in the shading. In the bump map, though, the lighter areas are lower while darker areas are higher, so leaving it as-is would create the opposite effect from what you're going for: raised shadows and sunken highlights. You can find the Invert function in the same place you found the Desaturate function, under the Image-->Adjustments menu.
You may need to tweak the bump map to increase the contrast between lighter and darker areas. Using it as-is may not create the depth of detail that you're looking for in your texture. You can use the Brightness / Contrast tool under the Image-->Adjustments menu to sharpen the image and increase the contrast.
Save the file--preferably in a lossless format with a high level of detail, like BMP / bitmap, though you'll need to check your3D program for image format compatibility.
Once you've created your bump map, all you need to do is import it into your3D animation program. Different programs have different ways of integrating bump maps into a model or polygon surface, but the controls for the bump map should allow you to define a range to make sure the raised textures and depressions don't extrude to extremes or scale down so small that they hardly show.
If you mean to save a project as Bitmap image, you can do that by going to File - Save As - *.bmp
