Mari7- some news you will not like so much. I worked on verse 2 and the second chorus today; during the verse, I came to a note that was lower than my low E. So I went and looked at the video, and he (Tim Landers) is playing a five string bass.
So here is verse 2 and the following chorus and fill.
Two options: Drop D tuning on your four string and a Drop D tab, or play a D that is an octave higher (at A5) instead of the low D (or even two octaves at G7).
I think both options would be fine, though the fretting is more movement in Drop D. But the tempo is not fast, so more movement is probably not a problem.
And here's the five string tab transposed to a 4 string in Drop D. Please let me know if this Drop D version works for you, Mari7, or if you find any mistakes. I think the fretting is mostly OK, but if this doesn't work, I could make a tab for 1 step down tuning (D G C F) which will play more like the fretting on a 5 string bass.