Although this may not ease your worry, the
ABD guides will normally give you packing instructions the day before your activities. Most people will have a backpack or bag (purse, tote bag, etc.) they carry on the bus with them. When you get to a location where you are doing an active activity, the guides will tell you if you can leave anything not needed for the activity on the bus. If you aren’t allowed to, ABD normally has a room or other location at the activity where your bags are stored until you finish.
I always carry my crossbody pacsafe bag with me. It has stayed on me when I have done bike riding and other such activities with ABD. Other guests have also worn their backpacks during such activities. However, when we did zip lining the zip line company assigned us lockers to put our things in. At other times, ABD has just instructed us to leave our bags in a specific place and they were there when we returned.
I know it can be nerve racking, but I’ve never had an issue with anything coming up missing when I’ve followed ABDs instructions about leaving my bag somewhere. You can always buy a money belt to wear to keep extra money, etc. in. You can also buy a waterproof pouch for water activities that you can wear. That way you have it in case you’re allowed to carry it when you do white water rafting.
Travel days are hard because you have all your belongings with you, but with careful planning you should be ok. Typically, your carry on and checked bag are under the bus unless ABD has already sent them to the next hotel.