It is not atypical use case to deploy Liberty-applications to IBM Bluemix. While you can do it in many ways, one of the better ways is to use UrbanCode Deploy to automate deployments to Bluemix.
This lab, Deploy Liberty application to Bluemix, describes how to do it. The lab is also a good introduction to UrbanCode Deploy as it starts by installing UCD and lab introduces the main concepts of UCD while going trough the use case of deploying Liberty-application to Bluemix.
So head to the UrbanCode Developer Center and check the lab. And all the other stuff.