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I trying to find out which one is correct.

That had been bothering me a bit for sometime. Or That had been bothering me a bit for some time.

And

I would have gone off anywhere at anytime to be with Ruby. Or I would have gone off anywhere at any time to be with Ruby.

Thanks
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Take a look at this definition:
http://www.merriam-webster.com/dictionary/anytime

As well as this one:
http://www.merriam-webster.com/dictionary/sometime?show=0&t=1288488482

Does that help you draw your own conclusions?
Comments  
1st question: some time (you're describing the "amount" of time you've been waiting, not the describing the verb or adding a "time" element to an action, as in: "Sometime I'd love to go to the opera with you".
http://www.grammarist.com/usage-errors/word-confusion/sometime-vs-some-time/

2nd: if you use it after "at" it's always separate.
Otherwise: anytime (any non-specific point in time)
any time= an AMOUNT of time (again, a characteristic of the time is important)

http://lawprofessors.typepad.com/legalwriting/2009/10/any-time-versus-anytime.html

I know you posted a while ago, but I hope it helps!