Can we migrate from one Git system to Another (e.g. Bitbucket to GitHub)?

Sure. Using Bitbucket to Github as example source and target systems respectively:

For each DataStage Project, the basic migration steps will be:

Create a new repository in Github, ideally, using the same name as the one in Bitbucket.
Register the necessary SSL credentials in Github so that they can be used by MettleCI Workbench and your build system (e.g. Atlassian Bamboo, Jenkins, etc) to access the repository.
Freeze change in the DataStage Project (i.e. no more commits from your team.)
Initialise the new Github repository with the contents of the old Bitbucket repository. The easiest option probably will be to change your local Git repository configuration to point to the new Github repository and perform the actions at the command line to push the whole of the local repository to the (new) remote.
Update the Project registration in Workbench to use the URL for the new Github repository.
Test that you can still perform commits via Workbench.
Update the Linked Repository details in Bamboo (including any new credentials).
Run the CI Plan for the Project to test that Bamboo is able to check out the contents of the repository.