The easiest way to achieve this would probably be the Jenkins Generic Webhook Trigger Plugin.
Once you have configured an inbound webhook trigger in Jenkins, you need to invoke it somehow. As is, the various curl based examples there could all be executed via Bamboo's Script task.
If you are wondering why a webhook is not yet amongst the supported Bamboo notification recipient types, you are not alone - please watch and vote for the following issue to further increase Atlassian's priority for this long missing and highly requested feature:
If you happen to use AWS, you could also work around the missing webhook notification type via the flexible Automate with AWS notification recipient in our (commercial) Automation with AWS (Bamboo) app, which offers various remote actions such as Invoke Lambda Function, which could then trigger the Jenkins webhook in turn.
G’day Bamboo customers, Bamboo DC 8.1 is now available with it the following features and programs: SAML 2.0, OpenID Connect, and Crowd SSO In order to help admins with a simplified user manage...
Connect with like-minded Atlassian users at free events near you!Find an event
Connect with like-minded Atlassian users at free events near you!
Unfortunately there are no Community Events near you at the moment.Host an event
You're one step closer to meeting fellow Atlassian users at your local event. Learn more about Community Events