Update Existing Records in Bulk

I need to update over 1,000 existing records using a script. I need to move all the data from old fields, into a new ones, and also add in information from linked records. Is there any way to do this? I have created a script that runs On Edit, which works, but I don't want to open up and edit each record one by one to trigger the script. I tried doing a bulk edit, but this didn't trigger the On Edit script. Any ideas?