Bamboo+Docker+Kubernetes deployment
I'm not familiar with Bamboo, but Kubernetes 1.2 will support the Deployment API, which will perform the rolling update on your behalf once you update the Deployment spec to the new image tag.
Alternatively, you could try Openshift 3, which is built on Kubernetes. It supports deployments triggered by image pushes:https://github.com/openshift/origin/blob/master/docs/deployments.md#triggers
I've faced a similar issue with a very similar build/deploy pipeline and I did end up having to output a properties file from the build step and make it a build artifact, that then gets read in by the deploy project.
There seem only to be a limited set of properties that you can access from a deployment project: https://confluence.atlassian.com/bamboo/variables-for-deployment-environments-342754180.html
Having said that, it is pretty easy to do the export:
In the build project export the properties you want into a file e.g project.properties and mark that as a build artifact.
Then in the deploy project, use the Inject Bamboo variables task, and the values will be available to the deployment project as
${bamboo.inject.<property name>}