I think a few things pop up here. You use a lot of words in slightly strange ways. I'm not sure that I'd ever use the phrase "playing out of key" - it doesn't mean much. What I hear isn't actually dissonance or out of key, or out of tune, or even wrong in a general sense - it's just, and this is my own opinion which you can happily discount, inappropriate. Bass can play, as a general conversation convention, a strong 3rd to create a kind of highlight - an oooh, interesting moment. Elton John does it in loads of songs, slapping a Major 3rd in the left hand to great effect. Look at "It's a little bit funny" when funny has the 3rd. You add in a 6th repeatedly - and there's nothing wrong with a 6th either, but then it sort of clashes when it drops to a 4th but the chord doesn't change. Normally this would be a suspension, but with the chord that means we have a 1-3-4-5-6 which is just a mess. You don't really change modes either because you don't really play moving lines, just different notes where perhaps 1-3 and 5 would be the 'normal' bass choices.
What I do know is that I'd never have dreamed up your bass line, and if I had to play it live, I'd find it difficult because with the rest of the band, I would feel that most of what I was playing is wrong.
Nothing wrong with new and radically strange bass parts if the part blends appropriately. That doesn't mean conventionally as you can stick in radically wrong notes and create something amazing when it works - look at some Jazz, where even when you look at all the notes being played you cannot work out what the chord is? Does it matter if it's good?
You say you are supposedly tone deaf? What would you say is tone deafness? There are clear parallels in the classical world. My pet hate is Stravinski's Rite of Spring, played by an amateur, multi-standard orchestra. The piece has so many 'wrong' notes and deliberate clashes and discords that when the players make mistakes, it's almost impossible to work out why!
In this music, the bass part is I think deliberately written to sound bad. Not so much the verses or the break - the notes and their sequence is pretty repetitive, but just the notes that clash with what the others are playing. Does it work? Frankly no, I don't think it does. The deliberate clashes. Are they musical? I think an argument could be made that they are, but I'd have to be kind of convinced by explanation. This is a bit like when you have to ask what a painting is, but then when you know, even though you don't like it, and would not have done it yourself, sometimes you understand.
I'm lazy, and I'm a traditionalist. As such, if presented with the track without the bass, and told to improvises a bass line using a Major 3rd as a feature - that would be fine, but it wouldn't have those other notes in it if I invented it. Too much no conformity for me.
If you are creating music for the masses, then "You're trying to write popular pop music. There's no reason it has to have dissonance" makes sense. Music has rules. Breaking the rules means it must have purpose. Breaking the rules just because you can means the audience may consider it a mistake, or just a bad song and that's a shame.
My piano playing grandmother told me that playing and side by side notes was a musical disaster and until my mid teens I believed her, until I started hearing Major 7ths and suspensions in some pop music and loved the character they added. My favourite chord ever - played with a Bb in the left hand and then these notes in the right hand going up - F-A-Bb-D then the same chord with the A dropping to G. Dissonance if you wish to call it that, but nice dissonance.