Attachment, connection, and transference are all different, and you can have one without the others. I am securely attached to my therapist and it has been so helpful in my therapy. My T and I also connect quite easily (I wouldn't call it "total connection" as you did--not sure what that is), but I don't have transference with my T (maybe a flash of negative transference once in a while), and I am not dependent on my T. Everyone has a different combination of these things in therapy, and what works for one person may not be ideal for another.

No, you are not bad for not wanting to be attached. I think it can be a good thing to know what one wants out of therapy. Although attachment can be very helpful, it may not be your cup of tea or what you need. I was not attached to my first therapist, and we got some useful work done. But it has been very healing for me to have a close relationship with my current therapist, and I'm not sure we could have that unless I was securely attached.