Is it of any use or benefit when I memorize the whole bassline, using the first method given in my first post?
I think you are asking what other methods are open to you.
Transcribing - playing by rote what has been written. The following talks about another method.
We learn how to transcribe one step at a time. Trying to memorize the whole bass line, what is meant by "whole"? The whole song or the bass line under a specific chord?
I want the chords first. Yes to the entire song, then I decide what notes of those chords I'll use. I rely upon the song's chord progression and then compose a bass line from that, i.e. I don't transpose I compose my own bass line based upon the chords used in the song. You can normally find the chords used from fake chord or lead sheet music and then failing to find any printed sheet music you can assume a chord progression. I-IV-V7-I has written a zillion songs.
Transposing you are hunting for the exact notes used by the original artist. I'm content on getting close, I really do not try and get the exact notes. Yes, I do want to have the correct chord progression to work from and then assume that the root, five, and eight notes will give me a safe bass line. If I need more I assume the correct 3 and or 7 could be used to fill out the chord tones. So instead of having exact sheet music I rely on some theory and get close. Why? Well give me the song title, the key and I can wing a pretty good bass line because I can assume what chord progression is going to be used with that kind of music. I'm not limited to playing by rote what someone else wrote. Understand this comes after years of playing, also understand I am terrible at transcribing individual notes of a song. But, using other methods I've been able to hold my own in several bands.
Like I said take this with a grain of salt. My music, Country, is dirt simple root five with chromatic runs to the next chord, so once I know the chord, the notes used are pretty predictable. Now if you are using some other style of music this may not work for you.
Then as has been said one of the "slow down" software programs will help, and I would recommend working on just notes to each chord, not trying to memorize longer bass lines than that.
Good luck.