My runners send out rhizomes in the Spring. Wouldn't hurt to check twice a year. They can travel pretty far from the parent plant. I am not sure how far since mine are in a rhizome barrier. I check to see if any have gone over the top of the barrier. I am not sure how deep. Others on the site have more experience then me.

If you're just trying to control the bamboo, you can do it any time of year, although early fall is good because most of the running for the year is done by then. Do it wherever you want to establish a perimeter. I've rarely seen rhizomes deeper than 8" on even ground.