I think that routine is the key.
I was terrified of going from the bassinet to the cot when DS was really little as we would rock the cot to settle him then walk out until he was unsettled again. We had been doing a bedtime routine and had a bedtime of 7 since he was about 2 weeks old but he would take some time and many resettles to get to sleep until he was about 3 months. It coincided with when I started a daytime routine but I think it was coincidence but one day I put him down and walked out and he was asleep 2 minutes later and that was it, every nighttime since then I just put him down, say goodnight and kiss him and he goes to sleep no dramas. It was as though he just realised what the routine was!