With the closure of https://jira.atlassian.com/browse/BCLOUD-19617,  we were introduced to this: https://confluence.atlassian.com/adminjiracloud/importing-data-from-bitbucket-935384618.html and https://support.atlassian.com/bitbucket-cloud/docs/export-issue-data-to-jira-cloud/ 

However, the attachments can only go through when you make the Repository AND the Issue Tracker both Public which raises potential security concerns. 

Attachments on the issue or on comments will only be exported if the repository and issue tracker are both public

 Suggestion

It would be worthwhile to consider allowing attachments to go through when migrating issues to Jira without making the repo+issue tracker Public.