My favorite bag for digital still camera, digital video camera or binocs is a insulated lunch bag smaller than a car battery. The bag should have a shoulder strap. If the strap is too short cut it off but save a few inches on each end to fasten a key chain ring or "O" ring so a shoulder strap can be attached. My bags all have external pockets so I can carry batteries, memory chips/video tapes, lens cleaning stuff and owners instruction book and/or bird watching guide.
Have a bottle of water and or a subway or bus map or a news paper protruding from the bag and you will look like anything but a photographer on the street.