Please use below report to extract the details of the controlled document record which is owned by a particular user.
[Controlled document Owner Information | Salesforce|https://url.us.m.mimecastprotect.com/s/ITNaC2k2vzt5442Inhjyf?domain=choicespine.lightning.force.com]
Once you extracted the controlled document ids, you can create a CSV file which contains the fields “id”, “OwnerId”. Here “id” is the salesforce id of controlled document which can be seen in above report and “OwnerId” is the salesforce id of user to whom you want to change the ownership.
Once the csv file is prepared you can bulk upload the data using data import wizard.
Please find below knowledge article on how to import data:
Import Data with the Data Import Wizard (salesforce.com)