A container on private property, like your driveway or a fenced commercial lot, needs no City permit. Give the driver a straight approach and firm ground and that is the whole requirement.
The City right-of-way is different, and Port Orange handles it through its Engineering Department. The two right-of-way instruments the City publishes are a construction permit, for anyone excavating in a public right-of-way, and a separate permit for communications facilities. Neither one is written for a container, and the City does not publish a dumpster placement permit, so do not assume the street or the swale in front of your house is open.
Call the City's Engineering Department at 386-506-5538 before you plan a street placement, and describe exactly where you want the container. The City's right-of-way page lists the applications the department receives and the person who handles them. City Hall is at 1000 City Center Circle and can be reached at 386-506-5500.
The bigger local question here is not the permit but who is allowed to bring the container. Port Orange requires a City franchise for anyone collecting construction and demolition debris inside the city limits. Your account manager will confirm both points, the placement and the franchise, before you lock in a date.
Before you book, confirm with the city that a container can be placed for your job at your address. Rules differ from city to city and they change. Your Prime Dumpster account manager will help you check, and will tell you plainly what your options are here.