A container that sits entirely on private property, on your driveway or inside a fenced job site, needs no city street permit.
Once any part of it reaches a public street, sidewalk or right of way, you need an encroachment permit from the City's engineering function inside Public Works. The City publishes an encroachment permit application and an engineering permit application together, along with an online route, on its engineering permits and applications page. City Hall is at 11999 Palm Drive and the general line is 760-329-6411.
There is a second, less obvious requirement in Desert Hot Springs and it falls on you rather than on the hauler. The City runs a construction and demolition diversion program. A covered project has to divert at least 50 percent of its construction waste, meet the state green building standard in force at the time, post a performance security with the construction permit application, and submit a recycling and waste reduction form to the Building and Safety Department as part of the permit process. Approval of that form is a condition of issuing any building or demolition permit, and no building or demolition permit is issued for a covered project until the City's compliance official has approved the waste plan.
Some work is exempt, including roofing projects with no tear-off, remodels under 500 square feet, plumbing-only, electrical-only or mechanical-only permits, seismic tie-downs, and projects that need no structural modification.
Before demolition, the City also expects a structure to be made available for deconstruction, salvage and recovery first, and recovered material counts toward the diversion target.
None of this is a reason to avoid a container; it is a reason to plan the paperwork alongside the container. Your account manager will tell you which City contact to use and how the diversion requirement interacts with your booking.