Honestly, I think a cover attracts more attention! I've been breastfeeding my daughter all over town for 9 months now. I don't use a cover, but I also do my best to keep discreet. They have nursing tank tops you can wear under your shirts so when it comes time to feed you can have almost zero skin showing.
I've never had people stare at me, make any sort of comments... most people really don't seem to notice.
Pumping extra to put in bottles is hard work. It's frustrating, time consuming and it can easily mess with the normal feeding schedule. Breasts don't have an unlimited supply, they fill up and the baby drains them. They then take time to fill up again. So what meal should my child skip so that I can have a bottle handy just in case she gets hungry while we're out? A bottle that, if unused, will likely have to be dumped because the shelf life isn't long. If baby will even take a bottle. If I'm around my baby won't have anything to do with bottles.