I found I had to adjust Dmitri's answer to ensure it works with images that don't actually need cropping (either horizontally, vertically or both)...
    public static Bitmap Crop(Bitmap bmp)
    {
        int w = bmp.Width;
        int h = bmp.Height;
        Func<int, bool> allWhiteRow = row =>
        {
            for (int i = 0; i < w; ++i)
                if (bmp.GetPixel(i, row).R != 255)
                    return false;
            return true;
        };
        Func<int, bool> allWhiteColumn = col =>
        {
            for (int i = 0; i < h; ++i)
                if (bmp.GetPixel(col, i).R != 255)
                    return false;
            return true;
        };
        int topmost = 0;
        for (int row = 0; row < h; ++row)
        {
            if (allWhiteRow(row))
                topmost = row;
            else break;
        }
        int bottommost = 0;
        for (int row = h - 1; row >= 0; --row)
        {
            if (allWhiteRow(row))
                bottommost = row;
            else break;
        }
        int leftmost = 0, rightmost = 0;
        for (int col = 0; col < w; ++col)
        {
            if (allWhiteColumn(col))
                leftmost = col;
            else
                break;
        }
        for (int col = w - 1; col >= 0; --col)
        {
            if (allWhiteColumn(col))
                rightmost = col;
            else
                break;
        }
        if (rightmost == 0) rightmost = w; // As reached left
        if (bottommost == 0) bottommost = h; // As reached top.
        int croppedWidth = rightmost - leftmost;
        int croppedHeight = bottommost - topmost;
        if (croppedWidth == 0) // No border on left or right
        {
            leftmost = 0;
            croppedWidth = w;
        }
        if (croppedHeight == 0) // No border on top or bottom
        {
            topmost = 0;
            croppedHeight = h;
        }
        try
        {
            var target = new Bitmap(croppedWidth, croppedHeight);
            using (Graphics g = Graphics.FromImage(target))
            {
                g.DrawImage(bmp,
                  new RectangleF(0, 0, croppedWidth, croppedHeight),
                  new RectangleF(leftmost, topmost, croppedWidth, croppedHeight),
                  GraphicsUnit.Pixel);
            }
            return target;
        }
        catch (Exception ex)
        {
            throw new Exception(
              string.Format("Values are topmost={0} btm={1} left={2} right={3} croppedWidth={4} croppedHeight={5}", topmost, bottommost, leftmost, rightmost, croppedWidth, croppedHeight),
              ex);
        }
    }