Git Submodules are implemented in Git and Bitbucket is not more than a centralized Git solution.
You should be able to use submodules when using Bitbucket. Note that you should add the submodule from your git client. You won't be able to do that in the Bitbucket web interface.
Atlassian even has an article about submodules in general: https://www.atlassian.com/git/tutorials/git-submodule
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