Does anyone's baby only fall sleep while nursing at night?

My baby girl will take a bottle at night but stil wants the boob. We can't put her in the crib until she's been asleep for t least 20 mins otherwise she will be wide awake. She sleeps at 12am or later. I'm trying to make a routine but nothing works. She is becoming dependent on the boob and I'm getting worried if I can't break that habit. I'm just SO tired that I nurse lying down. Like I have a cold right now and hubby is out of town and I barely slept last night? Anybody else have this problem? Help please!