Before I offer any suggestions, I want to say I think you are doing great. You've done a really good job at figuring out the notes. This is something a lot of people seem to struggle with, so give yourself a pat on the back. Although you have a good macro view, there is room to improve how you are playing the individual notes. If you haven't already gone through it, you may find this video helpful:
I suggest starting at the beginning and polishing small sections of the bass line. Start with the very first note. Notice how it is shaped. Consider the attack, decay, cutoff, and any variation in pitch. At first you consider and practice all of these things separately. But eventually the goal is to integrate all of them, which takes considerable practice.
I believe you are playing the intro on the right frets, but not necessarily using the best fingering. The first note F# has a little gliss (slide) down. The last note of the phrase (E) also has the little gliss down. Take a listen to the isolated track. Do you hear the glisses?
I suggest playing the notes with the glisses using your 4th finger. Try this fingering:
F# = 4 (9) [gliss down]
C# = 1 (4)
D = 2 (5)
D = 2 (5)
E = 4 (7) [gliss down]
First number is the suggested finger. Number in parentheses is the fret.
Let's dig a little deeper into the nuances and variation of this first phrase. I believe there may be an occasional hammer on from the D to E. I think its probably easier on the hand to play the hammer on using 1 to 4 rather than 2 to 4.
I added the hammer on in bold:
F# = 4 (9) [gliss down]
C# = 1 (4)
D = 2 (5)
D = 2 (5)
D = 1 (5) [hammer on to the following E]
E = 4 (7) [gliss down]
This fingering option is a bit tricky because you play the D with two different fingers.
You may prefer to do it this way, so you don't have to switch fingers on the same fret:
F# = 4 (9) [gliss down]
C# = 1 (4)
D = 1 (5)
D = 1 (5)
D = 1 (5) [hammer on to the following E]
E = 4 (7) [gliss down]
For me it's a bit of a challenging to play the shift from C# to D without making a squeak. However, I would probably play it this way if I weren't really digging into the weeds to try and find a better way.
Ultimately the best fingering is the one that works for you. So these are just different options for you to try.
Keep in mind, the original bass part does not play the pattern consistently. For example, the first note of the phrase also seems to occasionally have a hammer on from E to F#. As a developing player you may want to try and nail the part note for note. As a gigging musician, you would probably fudge it to some extent. IMHO that is okay and most likely the original player fudged it a bit live as well. It's up to you to decide how faithfully you will stick to the original bass line. I think it's important to really nail the style and feel, but not necessarily vital to play every little nuance in the proper time and place. YMMV of course.
There are lot's of other little nuances to dig out of this song, but I will leave that to you to decide how far down the rabbit hole you want to dive.
Have fun and good luck!