I ride every day, everywhere.
I often ride with DSLR or RF around my neck and 1 arm. You generally need to keep pulling it around to rest on your back, unless you have a strap that has a grippy rubber patch on it... like the ones that come with DSLRs....
Nice A&A, leather,rope etc, RF straps often do not have this, so they keep creeping around in front of your body, but I find that even when dangling there in front, I can ride in comfort, especially with a smaller lighter lens attached.
For colder weather times, I like having it around my neck, but under a zip up jacket.... if I need to whip it out quickly, just unzip my jacket and it falls out nicely...
For bags, messenger bags are the obvious choice, but I really prefer rucksuck/backpack type, because again, with a messenger bag, you have the same problem as a camera strap! They keep creeping around the front or to your side....
PS, I own a bike shop, and deal in a lot of types of bags for riding including messenger and rucksacks, and ride with cameras on many types of bikes every day... I am used to it, but for some people I am sure that constantly worrying about your camera, can be annoying. It never bothers me anymore.... My best suggestion is to have a strap which has a rubber patch on it, so that you can sling the camera as far around your back as possible, without it slipping back around the front...
Here are some of my older bikes.... I have no photos ready to upload of my current bikes...
🙂
http://4.bp.blogspot.com/_65_aiRx88Wc/SZuISmEg6sI/AAAAAAAABbA/z7BnLbIAiqw/s1600-h/IMGP4695.jpg
http://2.bp.blogspot.com/_65_aiRx88Wc/SZuGrveedwI/AAAAAAAABa4/lGVudi7nPSs/s1600-h/Image106.jpg
http://1.bp.blogspot.com/_65_aiRx88Wc/SSFurqavQFI/AAAAAAAABB8/GC5H3FmYDKg/s1600-h/IMGP2936.jpg
http://1.bp.blogspot.com/_65_aiRx88Wc/SOCvlQU1iEI/AAAAAAAAAxI/gqjn52gSquU/s1600-h/IMGP2461.jpg
http://3.bp.blogspot.com/_65_aiRx88Wc/SMT6JwOhaLI/AAAAAAAAApA/SE9OjSArWGM/s1600-h/naka5.jpg
http://4.bp.blogspot.com/_65_aiRx88Wc/SK911MW6vLI/AAAAAAAAAhg/Sge5veDOmCc/s1600-h/kiyo2.jpg
http://4.bp.blogspot.com/_65_aiRx88Wc/SK910nkkPFI/AAAAAAAAAhY/nhqCUtUPzZQ/s1600-h/kiyo1.jpg