How to setup Rider to use a (localdb) data source was not clear to me (and Rider IDE currently returns 404 for the help concerning database connections) so for others in the same situation, this is what I did in order to get access to my (localdb) in Rider.
From the Database tool window:
- Add a new data source using the 'SQL Server (jTds)' driver (not the 'SQL Server (Microsoft)' driver)
- Using the drop-down menu to the right of the URL select 'LocalDB'
- Enter your Database name
- Select an instance from the Instance drop-down menu
- Enter your Username and Password (or select to use Windows domain authentication)