If I bike in the city, I carry my cameras in a camera bag which sits in my backpack (a camera bag is an extra security measure). I'm planning to start a tour this summer, so been thinking on how to carry cameras and a transformer tablet. As long as I'm a photojourno, I will take 2 cameras and a set of lenses. The cameras are little system cams which I use and abuse a lot during different expeditions, so they are pretty sturdy and reliable, but small and not heavy at the same time. So, here are my thoughts on "how-to-carry-equipment" (at least how I see it before I hit the road. things can change on the way, so any ideas are appreciated).
1. One camera (as well as wallet, cards, batteries, phone and small stuff like a knife and a phone) comes into a waist bag with backpack straps. Got one on aliexpress, seems great and comfy with additional backpack straps.
2. The second camera, lenses and batteries come into a camera bag which is put into a front pannier.
3. The tablet goes to a protective hard case (which seems to be water resistant as well). Got it in a local supermarket for around 12$, but it seems sturdy. All this goes to the same front pannier.
+ batteries, chargers, cables and some more stuff come into the pannier.
So, the idea is that I have one camera with me all the time, so I can stop and put in out of the bag and shoot almost immediately. If the main camera gets f&!cked (if I fall or anything like that), I always will have the second one which is protected on the right front pannier.
Again, when getting supplies (so the bike is left outside a store), I have a small bag on my waist, so only one front pannier should be taken with me (to make it more comfy, a shoulder strap can be used). So, most expensive equipment and papers and stuff is always with me.
/ if you guys have any suggestions, please, let me know /

About dropping a camera. Just take one rule seriously - ALWAYS USE A NECK STRAP. Put it on your neck before taking a pic. It takes only 1-2 secs to put it on, but can save you some real $. It's just my #1 rule when shooting.

About stabilisation of an action camera. Try and search on the web. This year I met a guy who runs a videoblog about adventures, so he bought a stabilizer for a gopro. I tried it and loved it. Really good stabilization, comfy and the battery is great. Unfortunatelly, I don't remember the name, but I do remember that the guy bought in online in one of Chinese stores. The guy also told me that the same company produces stabs to use on bikes.

edit: found how the stab looks like https://chako.ua/upload/iblock/0e4/s...-for-gopro.jpg. the price on aliexpress is around 250$. suppose, more stuff like that can be found and maybe even cheaper.