Yes, SSR is accessible to everyone, but it's recommended to limit access to those who require Business Intelligence, Reports, and Self Service Reports (SSR).
Permissions on SSR Dashboards
You may also want to restrict who can create / edit dashboards - this is done in SSR using permissions at the document level.
See the article Setting Permissions for SRR dashboards.
The business Intelligence tab is not visible
If you find that the Business Intelligence tab isn't showing in the menu.
You can fix this via Module Access and check that Business Intelligence is ticked.
Head to User Settings.
Then go to Edit User Group.
Select Edit via the Action Tray on the Admin, or the Group in question.
Go to the tab Module Access.
Make sure Business Intelligence is ticked.
Save.
The general assumption is that if the user requires access to Reports they will more than likely require access to to SSR.
By enabling Business Intelligence, module access will automatically give access to SSR and any reports selected (ticked) within the Module Access.