A container on private property, in a driveway or inside a job-site boundary, is the normal arrangement in Trussville and it is how almost every job here is served. The city's own code is unusually relaxed about the rest, and it is worth saying why.
Trussville has no hauler permit, franchise or registration of any kind, and no hauler license. Its solid waste chapter runs to three short articles, on yard trash placement, littering, and the city's own collection service, and none of them regulates who may provide a container. Its businesses chapter was read in full, and it contains no waste or hauler class either. The only instrument that touches a container company here is the ordinary city business license, where garbage collection appears as a named occupational classification in the fee schedule. For a customer, that means there is no local approval to chase before a container can be scheduled.
What the code does do is require the container in the first place. Businesses generating more waste than two 96-gallon receptacles twice a week are required to arrange for disposal by use of a dumpster or other approved service. Apartment and mobile home park owners are billed differently depending on whether dumpster service is provided by the lessor, and the commercial fee turns on whether a business subscribes to a dumpster service at all. Private container service is written into the structure of the city's own billing.
There is also a published route off mandatory city collection, and it is worth knowing because it is not obvious. Anyone who wants to act as their own garbage contractor has to apply for and be granted a certificate of exception from the Jefferson County Health Department, and the certificate then has to be presented to the city clerk's office to be copied. The county reports periodically to the city on whether the conditions are being met. That is a county decision rather than a city one, and your account manager can tell you whether it is worth pursuing for your situation.
One practical note on placement. Nothing in the city's streets chapter creates a container permit, so the sensible plan is a private-property drop point agreed in advance. The city is strict about the gutter and ditch line for yard waste, and the same thinking applies to a container: keep it clear of drainage.