In JIRA a Link can contain anything you like, a link to another place as well.
In the wiki you can add links as well but if I understand it correct you'd like to have a link in Bitbucket to the Issue or Confluence page as well.
Similar to the link between a JIRA issue and a Confluence page when you add an issue link to the Confluence page. Correct?
Just have a look on the Documents add-on for JIRA. It may fully fill your needs: you can post as many links as you want to the project, by adding documents of type "URL". See https://marketplace.atlassian.com/plugins/com.stonikbyte.jira.plugins.project-docs-plugin
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