I'm new to horticulture, got 2 black bamboos a month ago, and seem to have a pest. I get little cottony (webs?) at the nodes, but not the black soot that indicates mealy bugs. There are white marks on the tops of leave, but no evidence of webbing on the underside (tho I admit I have less than 10x magnification to check for mites). And many leaves are browning at the tip, which may just mean I need to water more often. One plant has lots of new shoots, so I've cut back the old infested growth significantly. The other plant I'm trying to prune judiciously. Any advice?

You don't indicate your location/climate so I'm not sure which black bamboo you mean nor which pest you may have but...do not cut out any old growth until the new shoots are already making lots of leaves on new culms, after this it is fine to start thinning. I would blast the plants with a hose to try and dislodge the webs rather than cut the culms - you can always cut them later if needed but they are very valuable to a young plant.

Bamboo mites will make the white checkerboard type pattern visible on the top of the leaf, on the bottom of that leaf you 'mite' be able to see some webbing that you can rub off. I do not believe that bamboo mites will make webs at the branch/culm junctions, that is likely a different bug. I don't think mites will cause the brown leaves.

I'm in the Colorado Rockies, a 5a or possibly 4b climate, but the plants are potted and in a sunspace, living at a dry 40-90 degrees thru virtually the entire year. I have Phyllostachys nigra. The new shoots have some leaves, but I'll take care in the future not to risk loosing the plant. Before taking your suggestion of jetting water, I'm thinking of cleaning each shoot with a base-to-tip stroke of sponge wrapped around the shoot. As for the older growth, I'm spraying an advised detergent/oil/water mix lightly on all that growth and more intensely on anything that looks like pest development.
I appreciate all opinions and expertise. Thank you, BambooWeb, for hosting. This is a good site.

Indoors, ahh...it is my understanding that spider mites and other non-bamboo mites like dry air and sometimes it can be as simple as using a humidifier will cut them back. It sure feels weird though to be in southern Indiana in July and suggesting that someone run a humidifier.