You can reassign actions in bulk if you have the permissions to do so (if you go to the actions tab and don't see tick boxes next to them, you'll have to ask your administrator to give you these permissions).
On the actions page, tick all the actions you'd like to reassign - the actions that you want to reassign need to have the same person responsible, if you try to reassign actions with different person/s responsible you will see this message:
Once you have selected the assignments you want select the Tools menu drop-down and Replace Person Responsible.
Type in the user that you want replaced and the then the user that is the replacement and click on Save.