How does transcription end?
Termination  of  the synthesis of  the RNA molecule in bacteria is also signaled by  a sequence in the template  strand of the DNA molecule.
This sequence of nucleotide in the template strand is the RNA polymerase pause site. When the RNAP continues its transcription it reaches this site and pauses it's transcription activity over here. The longevity of this pause can also be affected by various factors like high $Mg^{2+}$ ions in some cases.  

Meanwhile, rho factor which after binding to rut-site, continues it's translocation along the mRNA (supposing mRNA is synthesized here) in 5'-3' direction using its ATPase activity. The rho factor utilises this opportunity when RNAP has paused it's transcription activity at the RNAP pause site to reach this ternary transcription elongation complex. When it had reached this complex it starts it's ATP dependent helicase activity which separates the RNA-DNA hybrid helix, causing the release of the mRNA.