"are there actual "bags" designed for this pupose, or do you just use a standard dry bag?"
Yes. Use the bag that best suite your situation.
What is in the bag will vary with where and how you use the boat, and if it will be in conjunction with a PFD ( only ) or raft, or dinghy.
Firmly keep in mind the purpose: To keep you healthy ( enough ) and to get found.
Everything about survival involves things being a consumable, including your health. ie: If you do not take drinking water with you, then you are limited to how long you can function without drinking water.
As a generic statement, you want signaling devices. This will include ( all or some ) a strobe marker, pyro signals, such as smoke/meteor aerial flares and/or HH flares, waterproof HH VHF, mirror, flashlight(s). Lung powered whistle(s) and horn, a compressed gas horn.
What you place in the first aid section is arguable, but DO include at the minimum the highest SPF, most waterproof sunblock.
I'll likely post more later. Let's see what others are doing...
-edit-
I never had an official ditch bag. What I DID have was often referred to as "a Captain's Bag". I and many around here often travel on other's boats, some of whom are still in the "learning" category, and we each carry our own Captain's Bag with us... So I had almost everything in the bag that was required by law to make a small recreational vessel "legal", such as my personal inflatable PFD, maps, HH plotting GPS, VHF, flares, horn, whistle, compass, a long sleeve shirt, Sunblock, ball cap, flashlight, personal EPIRB. Old pair of 'script sunglasses. Leatherman. 6way screwdriver. pliers.
In theory, except for lighting, the presence of that bag covered almost all legal requirements, and certainly would have provided enough for good navigation as well as survival tools. And it weighed "less than 70 lbs"
