Like most of us I have a few bags (and have owned many more since the days when I first started photographing in the mid 1970's).
For my "daily" bag, I use a Billingham Hadley (M6 TTL + 4 lenses + film + iPod + wallet, keys. Very comfy and easy to use. I had a Lowepro "Stealth Reporter" at one point (a large one) and it was a nightmare for the reasons the OP outlined.
I had (still have) one of the original Slingshot 300 bags but this also opened the wrong way round andstuff fell out as it was facing away from the photographer. I wrote to Lowepro about this to see if anything could be done to improve what was, otherwise, a great bag. At the next "Focus on Imaging" show, I went to the Lowpro stand and met up with the Product Manager. He explained that they'd just introduced a new range called the "Classified Sling" which, when slung round to the front, opens up with the enrance at the top and the hinge on the far side - away from the photographer. This makes it easier to get into and also feels like you can keep your kit away from prying eyes / fingers when travelling.
I have the 220AW version and my wife has the 180AW version. Great pieces of kit. Comfortable, practical and not "obvious" as being camera bags. Worth checking out.
Check out Kata as well, they have a few nice size shoulder bags that open the "correct" way. I was looking at a few in my local store recently although for some reason I can't seem to find them on their site right now. If I get back to the store again I'll try to get model numbers. They were really, really nice bags.
Bags I looked at were the Kata WS-604 and WS-606, sadly now discontinued. I may grab the 604 for my MF gear while they still have it.
Duhhh... Turn the bag around.
Originally Posted by benjiboy
That does not always work; the outside might have external pockets and you would not want them against your body.
Originally Posted by Leigh B
The bag I use has the top hinge on the outside top edge and works very well, it can be held down by a short velcro flap, and the zipper that holds it down properly has two handles so it can be zipped up either way, or both directions at once. The brand was "Oyster" although not marked as such, I bought it in the early 80s at Jessops, the branch in Holborn, London; I replaced the strap as it got threadbare but it's still my go-to bag: certainly got my money's worth.