Ahhh, memories. Thanks for that.
No. It is not Anaesthesia. It's an intro Cliff plays to For Whom The Bell Tolls and a few times during the Cliff Em All Video.
It's obviously newer or unrehearsed at the time of filming, as Cliff turns to Lars to tell him to count in the intro
At 3:37, I see Cliff banging away on an open E string during the verse riff of the song, and the only hammer on/pull offs I see are at the end of that verse riff.
I think Cliff doubles the guitar part at the end of that verse by playing their hammer on part. Thats what I used to do when we played it, and it sounded pretty much right.
If you look up the guitar notation and transcribe the guitar part at the end of that verse for bass, you should get it.
If you study your chord relationships and arpeggio's every day, you're half way towards unravelling the magic that is Cliff Burton
Have fun with it amd I hope I've helped you some.