I'm using the Cloud version of Jira. I found this article which refers to a JIRA Bitbucket Importer plugin, which I can't find on the marketplace and which hasn't been updated since 2015. It also refers to a "Bitbucket Import" link in System > Import & Export. But The link doesn't exist in my actual admin area.
You could try this python script that someone created to generate a csv file of you issues in Bitbucket and then use the csv importer in Jira.
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