Few Considerations to use Bi-directional sync with Lightning Sync:
1. “Sync both ways” sync setting option will only appear under Events, if you have Lightning Experience enabled on your Salesforce Org.
2. Events from Salesforce will only sync if they are created either from Lightning Experience (LEX) or Salesforce for iOS and Android. Events created or edited from Salesforce Classic don’t sync with Google/Microsoft outlook calendar.
3. If the Events are created in Salesforce using API like Workbench/Dataloader or through visualforce pages or synced using any other third-party integrations, they will not sync using Lightning Sync.
Check the below link for additional questions
