On private property, including your own driveway or a fenced site, no city permit applies to the container.
For anything touching a public road, street, or highway the city has a published route. Public Works issues right-of-way permits, and the city keeps a Right-of-Way Permit Packet alongside its driveway permit packet. Applications are taken in person at City Hall, Monday to Friday, between 8:30 a.m. and 12:30 p.m. and again between 1:30 p.m. and 4:00 p.m. Those two windows are worth noting before a late-week booking.
The code behind that permit is strict. Bonita Springs makes it unlawful to make any commercial use of the rights-of-way of a road, street, or highway, and its list of permitted exceptions covers special events, news racks, bus benches, utilities, and temporary loading where no off-street zone exists. A container is not on that list, which is why the Public Works route is the right place to start rather than an assumption.
Public Works, at 9101 Bonita Beach Road, takes those questions on 239-949-6246. The city publishes no fee or review time for the permit, so ask when you apply. If you are not certain where the right-of-way begins at your address, your account manager can get you to the right desk before delivery is scheduled.