Enable in-app notifications- It alerts users of activity in Lightning Experience and in the Salesforce mobile app.
Enable push notifications- It keeps users aware about relevant activity when they are not using Salesforce for Android or iOS.
Deselect Enable Salesforce Notification Banner- It removes the Salesforce Notification Banner for all users in your organization.
These above settings allows you to disable notifications at an org-wide level, but it doesn't provide control to disable the notification bell for specific users, profiles, or permission sets.
So there isn't any possibility to disable notification bell for set of users on profile or permission level.
Please refer Enable Salesforce Mobile App Notifications, Disable the Salesforce Notification Banner