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.
In case you want to transfer a local workspace to another computer that has no network access you can dump the workspace so you can then import it in the other computer.
Local workspaces however cannot be accessed by multiple users at the same time. If you need that, you'll need a TEAM subscription. A team workspace works pretty much like Dropbox, except it keeps a database in sync instead of files. Every computer accessing the same workspace still keeps a local copy of the database but the cloud infrastructure allows them to be kept in sync. Additionally, team members accessing the same team workspace can see data being updated in real-time on the app.