It depends on the type of garbage service in your area. The area I live in now requires each location to contract with a garbage service. You can take your own trash to the landfill but they charge by the ton and the minimum charge is one ton. There are several garbage services so there are several trucks running on various days. It is a very inefficient system. There are people who don't want to pay for garbage service. Many landlords find the garages or basements filled with garbage when the renters move out. Some throw their garbage on the roadsides or in wildlands.
I prefer a system where garbage service is included in the property taxes and handled by the municipality. They either have their own trucks and employees or hire one or multiple companies and give them specific areas. If the municipality owns the landfill, it doesn't matter to them which service brings the garbage in. If you have several garbage services, they might object to handling garbage from out of their area.
If one entity handles all of the garbage and it's just a matter of different days of service, they likely won't have a problem.
If you do pay for a certain company, call them and see if there is a place you can give it to them. Some businesses have a container that they don't fill and might allow you to put it there perhaps for a couple of dollars.