Our Cat is quite independent, however sleeps on our bed every night too. when we bought a Dog she was quite nasty and tried to assert her authority as being the oldest and the boss, so we were a bit worried...
This among other things was a reason to not co-sleep in the early months.

When we bought miss MJ home we were a bit worried, we had set the room up weeks before and after an initial explore that cat was NOT allowed in the baby room - kept door closed - prior to her coming home (same rule as the dog) and door is push to almost closed at night, and due to thinck carpet the cat cannot (but does not bother to) open it
Anyway, she was more aprehensive of Mj and kept out of her room when she arrived, occasionally when i would do a night feed she would come into MJ's room and sit near us, but leave if i got up.

As MJ has gotten older she has fallen in love with our cat, who really cat be bothered with this little thing that tries to follow her around
She will tolerate her pulling her fur and she seems to know that she is not allowed to hurt her.
In saying that i would not necessarily trust her and when she was small they were not left alone together.

Charlie (the cat) did retreat under the house for a week or two in the early weeks and i think bought us a bird and a mouse, we made sure that she was not forgotten and made sure she was always fed, patted and included in family time.

Now MJ will occasionally co-sleep with us, the cat is on the bed too, but keeps her distance and is not nasty at all.

HTH