bedtime routine

My son Brayden is 2 months today and we are trying to start a bedtime routine. He sleeps in a bassinet next to our bed so right now he generally falls asleep on my husband or myself around 8/830 after a feed and a story. We hold him or cuddle him while watching tv then bring him up and swaddle him w out waking whenever we go to bed. He stirs a little but mostly stays asleep. When did you guys start putting yours in bed and leaving to go back downstairs or do other things? I'm nervous to start even with a monitor but I know a more solid bedtime routine would probably be beneficial. He doesn't sleep through the night yet, he maybe makes it a max of 5 hrs in one stretch but usually its more like 3ish.