My understanding is that some of the smaller, desktop printers have a black-only or greyscale option. My R1900 that I use for Piezo has this. In the distant past some practitioners have recommended this as a serious B&W option, despite the warm tone you'll get.
The 3880 has a black option under Color settings : color or ABW or black. However the black option is greyed out for most media types. You'll have to lie to the printer about the media type, and you may have to choose an unsuitable one.
I've never done it, but I believe that you can print using QTR and just one black ink. You have to define a custom curve with just black and no grey or toning inks.