I didn't let my babies sleep in the bed with us. I didn't have a bassinet. I put the babies in their crib, in their room, on day one from coming home from the hospital. When they got older and I was no longer worried about them suffocating from us or from rebreathing I would sometimes put them in bed with me when my husband was away, particularly if they woke during the night or had a bad dream.
My youngest would not sleep in her bassinett either. I finally would give up and she slept on my chest for the first week. Only way I could get any sleep. She slept better in her crib. I did not use a bassinett with other 2 kids.