Now that there are no connections we can move the database. Depending on the situation it might be worth setting the database to read only or single user mode first. In my case, I had the application taken down so I felt confident no connections would be coming in.
With one line of code we can select the source and destination servers, the database name, specify that we want to use the backup and restore method, and then provide the path to a file share that both instance service accounts have access to:
The whole process is just five lines of code, so it could hardly be easier.