On private property, including your driveway or a fenced job site, nothing in the city's solid waste rules requires a container permit.
The city's streets and public places chapter was not part of this review, so instead of assuming a right-of-way route exists, treat a street placement as a question for the City of Rocky Mount before you book. Your account manager will find the contact for you.
What the city's rules do say about the street is helpful rather than restrictive. Leaving solid waste on a street or on city property is an offence, but the rule closes by excepting waste that is placed in a designated location or in a solid waste container. So the container is treated as part of the answer to the offence, not as the problem.
The city also has a spillage rule that names exactly the materials our customers load, covering dirt, rocks, sand, brick, broken concrete, lumber, tree trunks, limbs, cinders, plaster, gravel, paper and cardboard. Nothing may fall, scatter or blow from a vehicle onto a street, and anything that does has to be removed immediately. Importantly, the city sets no vehicle construction standard at all, so there is no requirement for an enclosed or compacting truck here. A properly tarped open-top container on a tilt frame satisfies Rocky Mount on the published words, which is not true in every city.
One rule does land on you rather than on us. The city requires construction, demolition, land clearing and landscaping debris to be collected, removed and disposed of by the contractor or builder, and if they fail to do it, by the occupant of the property. So arranging a container is the property owner's obligation in the city's own words, not a discretionary extra.
Anyone collecting or transporting solid waste in Rocky Mount also needs a permit from the director of public works. The city publishes the requirement but not its terms, so that side sits with us, and your account manager confirms it is in place before delivery.