This is a new pattern which I’ve learnt recently, although have heard it many times.
So this is used in a case, when the Speaker is wishing/ wondering about something. In this case wondering whether the bus will arrive early or not.
But why does it say 来ない and not 来る？
The other example was 実験がうまくいくかな。 I wonder/ wish the experiment goes well. This was easy enough to understand.
Thank you
Since 来ない is the negative, I’d guess that it’s because the state of the bus is uncertain. So in this context it’s presupposed that the bus isn’t coming, but they’re wondering if it will?
かな turns the sentences into questions or musings.
The other example was 実験がうまくいくかな。 I wonder/ wish the experiment goes well. This was easy enough to understand.
I’d translate this as “I wonder if the experiment will go well?”
Or the other sentence, “I wonder if the buss won’t come soon?”
Thank you.
So with this logic, can we also modify and say that,
実験がうまくいかないかな。Meaning that the person is not that confident about the experiment and he knows that it might go wrong too.?
Thank you.
“I wonder if the bus won’t come soon?” this doesn’t sound correct, right?
Well, there’s the negation that @Joeni mentioned 来ない that gives it that double negation feeling to it.
実験がうまくいかないかな with this you again end up with a double negation. I wonder if the experiment won’t go well?
I guess there are more natural sounding ways of expressing it in English (it feels convoluted), but is sounds natural in Japanese.
Edit: I always think of “ka na” and “ka” as something you just attach at the end of the sentence. You first make a sentence, and then decide if you wanna turn it into a question by ending it with “ka” or “ka na”. It’s like an afterthought.
It doesn’t work like that in English.
Okay.
So, both these sentences would mean the same.
バスが早く来ないかな
バスが早く来るかな
So can it be said that when the person is double negating in this situation, he knows that there’s a high possibility that the Bus won’t come early, but still he is wondering that for a change or once, it will come quickly?
We’d probably say “I don’t suppose the bus is coming soon?” as the closest equivalent.
Thanks! That’s much better, and still has the negative in there. 
We Brits are naturally pessimistic, hehe
I think in Swedish, it’s be a bit accusatory, like “Jag undrar om bussen har tänkt att dyka upp någon gång?” (as if the buss was sentinent and was deliberately being annoying by not arriving immediately) 
Interestingly, you can say almost precisely that in Swedish:
“Jag undrar om inte bussen kommer snart.”
There are some similar patterns in English, too:
“Won’t the bus come soon?”
“The bus wouldn’t happen to be coming soon?”
“I don’t suppose the bus is coming soon?”
While Japanese and English are so distinct from each other that there probably isn’t much of a connection, but using negative forms to soften expressions or express wonder appears to occur in quite a lot of languages, n’est-ce pas?
Edit: I swear this post was somewhat original when I started writing it, but writing at work makes me go at about one sentence per hours 
Well thank you all for the explanation.
I think the nuance is this: ‘Won’t the bus come soon, I wonder?’, which is how I would translate バスが早く来ないかな, has the implication that the speaker is hoping for/expecting the positive outcome. That aside, I think everyone else has explained the other aspects of this structure, so I believe my work here is done.
Ha ha ha, but still, Thanks anyway. 
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