I am trying to understand the application development life cycle for IBM bluemix application development. The bluemix document mentions about using Git, Eclipse or CF to push the application to bluemix cloud. I would like to know if I can develop the full application in the local environment, with connectivity to bluemix cloud?. I want to develop it locally and test it, before I can deploy/push into the cloud.
First you have to create a Git repository for your application. You can do it clicking on the "Add git" button within your application dashboard (it will create your repo in IBM Bluemix DevOps Services) or you can just create manually your own repo (e.g. on GitHub) with the starter code of the runtime you chose. Once you have created your repository, you can clone it on your local machine using the git clone command. This allows you to work on your local copy, testing it on your machine.
Your application will have probably some services bound to it, so you should decide which services you want to replicate in your local environment and which services you want to use remotely (e.g: you might want to connect directly to your SQL DB service instance on Bluemix or you might want to create a local version of the DB on your machine). Please note that some services could not allow remote connection from your local environment: refer to the docs of each specific service you need.
Whatever you decide you can develop and test the full application on the local environment. Once you have finished you can use the git push command to deliver your changes to the repository and then use the cf push command to deploy your application to Bluemix.
Consider that if you need to automate your builds and deployments you can take a look at IBM Continuous Delivery Pipeline for Bluemix. You can also use it in DevOps Services.