I usually play along with the original on repeat to get it into my head.
How exactly I follow the bass part depends how much of a feature it is.
For example, we were working on Elton John's 'Saturday Night's Alright For Fighting' before the fun stopped. Dee Murray played some rather funky little runs, but seeing as I am singing the thing as well, I thought it best to keep the bass quite simplified and tight, seeing as the world will not notice anyway.