Hello @Jon_C 
welcome to the forum!
You should be able to connect to the db when your database is reachable over the internet. It will not be enough when you can access only the machine via ssh.
To connect you need at least to know the Domain/ IP, port authentication method and credentials on which your DB is running. The standard port will be 27017. In case the database is reachable via the internet, you should be able to connect to it via the mongo shell and / or Compass.
The mongodb documentation describes very good the connection options to a remote database or replication set.
I also might be an option to look into MongoDB Atlas you will get a free account for (I think) 512 MB, including lots of infrastructure benefits. So if there is no strong urge to run MongoDB on your server, Atlas might be the less stressful option.
Cheers,
Michael