J., I gotta ask, what is bumping? At first I thought you meant pump...
I successfully nursed and gave bottles with both of my children. My older son was 4 weeks old when I got terribly sick, throwing up with a high fever, and diarfhea too. My doctor told me not to nurse. However, it came on hard and fast in the middle of the night, and I was so sick that I couldn't put him to my breast without throwing up on him. My husband went and got the ONE bottle we had with the sample of formula they gave us at the hospital, and made a bottle. My son sucked it down with no hesitation.
My second son had trouble gaining weight at the beginning. He took a very long time to nurse, but it wasn't until he was 4 years old that we understood why he had a hard time - he has a submucous cleft palate. That's a structural defect, and sucking hard was something he couldn't do. I started supplementing with a bottle right out of the hospital. I continued to nurse, and he took both breast and bottle.
I know that La Leche would tell you that if you MUST give a bottle, to wait for a long time. I disagree. I would start out as soon as you get your nursing established, like a week. I'd give the baby the bottle in the middle of the night. Babies are a lot more picky during the day. If baby doesn't want it from you, give the bottle to your husband. (I didn't have to do that. They both took bottles from me.)
Good luck!
Dawn