I placed the fallen part into a small vase of water no slicing or cutting of any type and it is still alive and seems to be doing very well after a month staying as white as it was when placed. If I keep it the way it is and do what I must will this small piece root ?

The parent bamboo is over four years old and it has only had one spell of yellowing leaves in the first year ( six leaves ) we got it and it did seem to want to recover from that on the next yr as of current it looks real good even with the missing piece.

Is it odd to have a piece fall out with a light dusting finger brushing from a lucky bamboo that looks like new at age 3+ with such ease ?

Parent plant stats:
Ceramic holder a real big round holder vase, white colored gravely type pebbles small in size, filter water preboiled and cooled down watering , never been fertilized, 23 upright stalks 24
+/- inches high 10-12 pounds in weight. It's six yellowing leaves where well pruned out last yr it never again got any yellowing sence, indoor grown. I tend to move it around for good to dim lighting and ideal room/ bay window temps on a quarterly basis.I also scrub the holder and rocks on this quarterly basis with dawn and five time rince with regular water..

With this in mind am I doing good or can I do something better ? If you reccomend fertting I insist on only organic methods any non organics need not even be mentioned I just wont buy em. Thank you for understanding.
Wes