I too usually bury the runner and cut it after they root.
If the swords runner is growing up toward the light, I usually let the baby plant get 4 or 5 nice leaves before cutting. When they grow up they will also start to show roots looking for the substrate...another good time to cut.
I have 3 types of Amazon Swords...none in which are they same plant yet all were sold as an Amazon sword. Which do you have?