Azure Service Bus Emulator
This has been a long-standing issue, so I think it's worthwhile to offer an update to the state of things right now.
There isn't a local emulator available for Azure Service Bus yet, however some people have started upvoting this github ticket on the Azure Service Bus project.
If you've landed on this issue and are looking for an emulation option, I urge you to put your upvote on the original problem description.
As far as I know, there is no Service Bus emulator. A feedback on UserVoice is open at https://feedback.azure.com/forums/216926-service-bus/suggestions/2565564-provide-a-service-bus-emulator-on-a-local-computer and a GitHub issue at https://github.com/Azure/azure-service-bus/issues/223. Don't hesitate to upvote and subscribe to these feedback channels.
However, the Azure Storage Emulator includes an emulator for Azure Storage queues if this can be an alternative: https://azure.microsoft.com/en-us/documentation/articles/storage-use-emulator/
If your run your Web Job code locally, the WebJob trigger might be able to connect to the local Azure Storage Emulator. Please see https://azure.microsoft.com/en-us/documentation/articles/websites-dotnet-webjobs-sdk/#workerrole