This probably isn't the complete answer as I don't know so much about eukaryotic transcription, but maybe I can start the answer.
First of all DNA bending can be sequence dependent - the double helix is not intrinsically straight. DNA is also pretty easy to bend - it spends most of its time coiled pretty easily around histones, and eukaryotes, supercoiled into chromatin.
In transcription though, there are proteins that come along and effect bends in the DNA or even tight loops, so that the transcription initiation complex (TIC) can be activated by transcription factors (TFs) upstream as the DNA flops over.
see this happening in this video at about :40:
I think in some cases there might be other proteins bound upstream of the TIC to make the influence of various TFs greater. I know in highly regulated genes (such as developmental genes in animals) transcription regulation can be impossibly complicated with lots if internal logic. The classic example is ENDO16 from sea urchin (see second image) which has scores of protein binding sites in front of it.
I was told that DNA binding proteins find their binding sites at a rate faster than diffusion. The prof told me that she thought that there might be a tendency to diffuse along the length of the DNA because of its charge. I have no reference for this, but it might help answer your question as to how the NRs pair up so quickly.