Though it isn't talked about and isn't recommended...
BFing, co-sleeping moms find that they naturally end up sleeping on their side facing their newborn and the newborn ends up sleeping on his/her side facing mom. It happened with both my kids, too. And I've seen it time and again on here.
There is nothing bad about side sleeping. In fact, in the original Back to Sleep campaign that got babies off their tummies, it was Back or Side to Sleep. But that was too confusing so they went to Back to Sleep.
The important things for co-sleeping:
Make sure your bed clothes are all pulled tight.
Don't use a head board or foot board on your bed (my bed is just box spring and mattress on the floor which is best)
Keep bed pulled away from the walls so baby can't get caught between the bed and wall.
Keep pillows far away from baby (ideally you wouldn't even use a pillow)
Keep blankets well away from baby (ideally you wouldn't use a blanket)
Make sure the baby does not sleep on his/her tummy on a soft mattress.
Don't wear any clothes that are overloose or have cords on them (that might cover baby's mouth or get tangled with baby)
Of course, not all of that is possible. My solution was to follow all of it except the pillow and blanket. However, I use only one small pillow for me. I keep it as far from baby as possible and just use the end of it for my head. The rest is away from baby's sleeping space. I dress warm and use a light blanket (even in deep winter). I keep my arms and top dressed warm so I don't have to pull the blanket up past my waist. Baby sleeps by my chest so the blanket is not pulled over them. A thermal, long sleeved top with buttons down the front is perfect. It keeps me warm and can be unbuttoned for boob access.