I have created a custom contact type with a several fields. Can I use the new bulk update process to update/set these fields? 

When looking at the new process I see a section for Import Profile and Settings, but I don't see anywhere I can add additional headers to map. 

Hello Kenneth,

I believe you should still be able to upload your new contact list and it should even try to match and merge existing contacts. You can find more information at the following Resource Center article:

https://help.mypurecloud.com/articles/perform-bulk-import-external-contacts-organizations/