I'm not sure that I'm bonding with my baby. Isn't this something that's supposed to happen automatically?

Its said a baby bonds with the mother from the womb and activity like breastfeeding only increases it. Some babies are not as reactive or responsive but that doesn't mean they aren't bonding with you. I suggest spend more time with your baby doing the above activities suggested by Stan and Diana. You can also go through this interesting article on bonding with your baby- http://sg.theasianparent.com/ways-of-bonding-with-your-baby/