There are various propagation techniques for bamboos, and ones like black bamboo can fairly easily be done by "major division". For a major division, you want each part of the plant to retain about 3 culms and a decent share of the rhizome. It is often recommended also to shorten the culms by about a half, as the damaged rhizome is less able to support the culms.

The danger of cutting off a division too small can be seen in one of mine which still has just one tiny culm about 8 years after I did it, it never got going, though somehow it doesn't die either. I wonder when if ever it will make its mind up.

There are propation techniques which work with smaller pieces of plant - minor divisions and rhizome cuttings, but they require more care and attention to take than just shoving them in a hole in the garden, and also take longer to give a worthwhile plant. Specific species are easier/harder to propagate, but black bamboo is one of the easier ones.