After all, the image needs to be cleaned.
In GIMP you can use the Select By Color tool with a threshold of e.g. 30 and select the background:
Delete the selection with del key and un-select with Shift-Ctrl-A:
Scale the image to the desired size using a proper interpolation algorithm:
Note that now the drawing is very little:
In order to obtain a black and white image you could apply the Threshold tool (in Colors menu), but you can loose the red border or the detail of the image:
Perhaps is better Desaturate (in Colors menu) the image before to apply the threshold:
Now the image is a little better:
Before exporting the image, you must transform it in a black and white one changing the mode to indexed (Image menu):
Now you can export it to BMP.
Please note that the result of the print may depend on printer settings and printer driver. For certain kinds of printers you can send directly a bigger (and more resolute) image, and they will adapt it to the label format.