Everything you do here writes to Bullhorn immediately. No export, no copy-paste.
From one profile
Open the profile (View Profile), then click Add to at the top right of the profile header and pick Bullhorn Job, Tearsheet or List.
Bullhorn Job, step 1: search for the job and pick it.
Step 2: pick the submission status. The list is your account's Bullhorn statuses (Submitted, Candidate Interested, Client Rejected, Offer Extended and so on). Click Continue.
The candidate appears on the job's Submissions tab in Bullhorn with that status.
Tearsheet: pick an existing tearsheet or create one. The candidate is added in Bullhorn.
List: a Candidately list, for longer-term pools.
From several results
Hover the result cards, tick the checkboxes, then Bulk actions in the top bar: Submit to Bullhorn job, Add to Tearsheet, Add to Shortlist, Add to List, Hide from search. See Bulk actions.
From Bullhorn
In the Candidate Search tab on a job, the same buttons are available. Submit to Bullhorn job defaults to the job you are on.
Notes
Submissions use your Bullhorn workflow statuses, so the status dropdown reflects your account's setup.
The action is logged on the Bullhorn record like any other submission.
If the candidate is already on the job, Bullhorn's own rules apply; you won't get a duplicate submission.