You don't need a dedicated camera bag, but they can be very nice. And sometimes it's nicer not to have a bag at all.
I assume you're talking about shooting from the bag, not transporting. For shooting out of the bag, a backpack can be a real pain. For transport, either in a vehicle or on your back, they're great. There are some sling-type bags that rotate around, but I feel weird leaving gear on my back where I can't see it, as opposed to under my right arm where I can immediately feel it. It's a security thing, but I live in the 3d world and am a security officer by trade (read: paranoid).
If you already have a non-photo messenger-type bag, maybe buy some inserts for it and try that out. Or just toss the gear in as best you can, maybe wrap it in t-shirts. No need to get fancy until you know if you like it or not.
Or get a satchel or courier-type photo bag (Courierware/bare bones, Lowe Classified, Domke, ThinkTank, whatever) that you can use for a laptop or whatever if you end up not using the bag purely for photography. Or just find a cheap off-brand, even if it's not camera-specific, and give it a shot.
Lotsa "or"s in this one. Good luck.