No matter the plan you use, BOMIST always keeps a local database. Essentially, this consists of a folder somewhere in you file system.
When you create a local workspace you specify where you want it to be stored. This way, if you want to share a local workspace between computers, all you need to do is to make sure you keep it in a folder accessible from all computers you intend to use, whether it's a Dropbox folder or a folder in a local network for example.
Local workspaces however cannot be accessed by multiple users at the same time. If you need that, you'll need a TEAM subscription. With a TEAM subscription, BOMIST deploys a database on the cloud responsible for making sure every user accessing a workspace is in sync and is able to see changes in real-time.
In case you want to pass a local workspace to another computer that has no network access you can dump the workspace so you can then import it on the other computer.