On private property, including your driveway or a fenced job site, Rockville's solid waste rules impose no container permit, and the word dumpster does not appear in that chapter at all.
The city's streets and rights-of-way chapter was not part of this review, so instead of assuming an encroachment route exists, treat a street placement as a question for the City of Rockville at 111 Maryland Avenue before you book. Your account manager will find the right contact.
What Rockville does regulate heavily is the collector, and one of its rules reaches your schedule directly. The city bars licensees and their employees from collecting, picking up or otherwise handling refuse or refuse containers between 9 p.m. and 7 a.m. Monday through Friday, and between 9 p.m. and 9 a.m. on Saturdays, Sundays and federal holidays. Because the rule names containers and not just refuse, a delivery or a pickup of the container itself falls inside that window, so early morning drops before 7 a.m. are not available in Rockville and weekend drops cannot start before 9 a.m.
The rest of the city's regime is ours to satisfy rather than yours. Anyone collecting or transporting refuse in Rockville needs a license from the Superintendent of the Division of Licenses and Inspection, applied for by 1 July each year and expiring on 30 June. It requires a bona fide office in the Washington metropolitan area where bills can be paid, a bond or cash deposit held by the Director of Finance, a current list of every vehicle by description and serial number, lettering at least three inches high on both sides of each vehicle, and a filed list of employees with a contact reachable at any hour. Those licenses cannot be transferred.
One useful right sits alongside all of that: Rockville expressly allows the producer of the refuse, or the owner of the premises where it accumulated, to collect it themselves. So a homeowner hauling their own debris is on solid ground, and a container is a convenience rather than a legal necessity.