The normal setup is that you should integrate your SCM with your Bamboo to automatically build when a commit/push is made. Another concept to follow is to make sure that you commit messages have Jira issue keys in them so that they can be linked back to your issues.
But to answer your question specifically, I have not seen an add-on that does what you want. Maybe other's have seen one like that.
One other option is to use Jira's Webhooks to call the related Bamboo Plan.
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