Amazon EventBridge is now available in AWS Middle East (Bahrain) Region

Amazon EventBridge is a serverless event bus that delivers a stream of real-time data from event sources, including SaaS applications like Zendesk, Datadog, and Pagerduty, and routes that data to targets like AWS Lambda. You can set up routing rules to determine where to send your data to build application architectures that react in real time to all of your data sources. EventBridge makes it easy to build event-driven applications, because EventBridge takes care of event ingestion and delivery, security, authorization, and error handling. 

Please see the AWS Region table for all the regions where Amazon EventBridge is available.