"Ik zal de bus hebben genomen."

It doesn't matter. Ik zal de bus hebben genomen and Ik zal de bus genomen hebben both work, it's a matter of personal preference which order to use or to use both. Maybe there are some regional changes as well, but I'm not sure about that.

"Shall we dance?" can be paraphrased rather easily; transforming it through use of a less archaic verb form than "shall" cannot be performed so easily. "Might we dance?" is a possibility, though "(S)hall we dance?" still seems current.

Person A: Shall we dance? Person B: Let's Dance. = good; We shall dance. = odd; Let us dance. = only slightly odd, though somewhat formal; Shall we, indeed. = intriguing, notably with respect to the level of enthusiasm intended as well awareness of the oddness of the word "shall"; Let us. = practically reasonable.

Might we indeed.

I still remember how the Teach Yourself language book series often had a way of making UK English words not generally used in US English rather salient; possibly using I and We "shall" especially in the older works; and also often indicating French cognates or grammatical contrasts in books for learning languages other than French, especially in the older ones, with the cognates often indicated after "cf." It even made me think that "cf." meant "cognate of" or rather than the Latin for "compare to".

then you should study tenses better, I had this at school. this construction means that the action will have been completed by a certain time in the future.