This is what I did yesterday! I plugged in, had the first few second of the song on repeat - played the part over and over with different notes and rhythms, then jotted it down in MuseScore and boom - I had written the first 10 or so bars down and I think it sounded pretty good. Nothing complex, just some staccato 8th notes etc.
The added benefit of midi is that it's pitch-perfect and it's easier to be certain which notes work well together and when you are out of harmony. With real bass it can sometimes be hard to tell, especially as you go up the neck and if your intonation is a bit off. It can all become a confusing mush.
Anyway I just heard the track and like most chiptune music, it's very chaotic without actual natural space for bass guitar so no wonder it's confusing. If you pay attention even the midi bass on it is doing what you tried, staccato 8th notes that do nothing but shift the root.
You can also try doing quarter note walking, think ska/reggae triads (root, third, fifth, root or other combinations) when it changes into those fast piano pedal notes.
