A bamboo division can take at least a year to show any progress...sometimes more. The fact that yours has even a tiny shoot at this point is a good sign. Keep it watered and let it do its thing. Just don't expect miracles. It needs time to get established. It will be several years before you see any shoots that are as large as the cut one.

thanks! im just worried that it won't get much of a root system before any cold hits i think i will mulch it heavy and put a tarp over it in the winter. i read it would take years and years to be established i didn't expect any top growth until next year but this is a surprise. from what i brushed off the top it looks like there's no new root growth so im just baffled i will just hope and wait it out and see it hopefully come along in the years.

What gardening Zone are you in?

the edge between 6 and 7

last year was our first really cold winter rarely we drop below 20

It should be alright. It's not a bad idea to dump some mulch on it in the fall for protection, but a tarp is only necessary in really cold zones to protect culms and leaves. Don't put high nitrogen fertilizer on now as it will stimulate aboveground growth at the expense of the roots. Black bamboo is hardy to about -5F but the foliage can be damaged at temperatures as low as about 10F.

Moisture and nitrogen are two things bamboos love. Whereas they don't like dryness and infertility much, except for certain kinds adapted to climates that are quite droughty for part of the year.