From what I've read and been told, everyone develops that connection at a different pace. I feel like I have a good bond with our little girl but I still have that feeling you're talking about - that when I'm dead tired and stressed out I'm only feeding her because I need to, not because I want to. This morning I had an immensely difficult time getting out of bed to take care of her while she was fussing. It gets to the point where I worry about my ability to do what it takes, but I know that I will be able to even if my body is just running on auto pilot.
You're not alone in how you feel, believe me! And just try to spend time cuddling or "playing" with baby. One of my favorite things is when we do tummy time in the evening - when she's awake and I'm at my best each day. I love watching her and cheering her on as she tries to pick her head up and look around or move her head side to side. If you find an activity that you enjoy with your baby, do that - it might help you feel that "connected" feeling more.
And you're not a bad mom if it takes a while :)