Okay, okay, here's what you need.
First off, you'll need the transformation interaction.
You want it to last 12 hours and have a cooldown of 24 hours. Now, keep in mind that time works differently in adventure mode and fort mode. 600 ticks is half a day in either mode, but in adventure mode that'll last you until the next town while in fort mode it'll be over after about ten (real time) seconds... which should still be enough for one quick battle.
You can extend it by using the DWF_STRETCH tag, which will increase its duration in fort mode, but we'll work with that later.
You wanted it to start after 10 seconds, but what time scale do you actually mean? The shortest 'syndrome timer' possible in adventure mode is 72 ticks (this will happen if you give it START:1), and in fort mode the whole transformation will only last for 10 real-time seconds, so it's hard to judge. I left it out for now.
My advice would be to not use regular WAIT_TIME for this interaction, because cooldowns can't be adjusted between modes and long-term cooldowns can be kind of wonky and unpredictable in adventure mode (I think they might not tick down while you're in fast travel). Instead, use a syndrome class that prevents the transformation being applied. This can also be used to prevent other transformations if you want, so someone can have many transformations available but will still be limited to one per day.
For the probability transformation, this is also possible and has to do with the way transformations are applied. When multiple transformations are applied to a creature, they all "take effect", but only the first one will actually be applied (since a creature can only be one creature at a time). If the timer on the first runs out while another transformation is "active", they will transform into the second creature (not needed here, but good to know). So, by making the giant bear transformation 20% first, then the regular transformation 100%, they will have a 20% chance of transforming into a giant bear, and if this does not happen they will become a regular bear. (You can layer this as much as you want to make a 'random polymorph' spell.)
Also, when you use probability syndromes, make sure to separate them into different syndromes. Otherwise problems can happen when you load a saved game (any syndrome with an active effect will apply all of its possible effects when a game is loaded, ignoring probabilities).
[INTERACTION:MORPH_BEAR]
[I_SOURCE:CREATURE_ACTION]
[I_TARGET:A:CREATURE]
[IT_LOCATION:CONTEXT_CREATURE]
[IT_CANNOT_HAVE_SYNDROME_CLASS:MORPH_COOLDOWN]
[I_EFFECT:ADD_SYNDROME]
[IE_TARGET:A]
[IE_IMMEDIATE]
[SYNDROME]
[CE_BODY_TRANSFORMATION:START:0:END:600:PROB:20]
[CE:CREATURE:GIANT_BEAR_GRIZZLY:MALE] <-- There must be a caste unless you make a custom, sexless creature. You can make more probability effects to make it random whether you transform into a male or female, if you feel the need to do so.
[SYNDROME]
[SYN_CLASS:MORPH_COOLDOWN]
[CE_BODY_TRANSFORMATION:START:0:END:600:PROB:100]
[CE:CREATURE:BEAR_GRIZZLY:MALE]
[CE_SKILL_ROLL_ADJUST:PERC:100:PERC_ON:0:START:0:END:1200] <-- This does nothing, but 'holds' the syndrome until the 1200 ticks are expired, ensuring that the MORPH_COOLDOWN class is still active.
[CE_FLASH_TILE:TILE:25:5:0:1:FREQUENCY:500:60:START:600:END:1200] <-- Makes an arrow flash when the creature cannot transform. Not necessary, but helpful for adventurers.
For the secret, use this:
[INTERACTION:SECRET_BEAR]
[I_SOURCE:SECRET]
[IS_NAME:the secrets of bears]
[IS_SPHERE:ANIMALS]
[IS_SECRET_GOAL:IMMORTALITY]
[IS_SECRET:SUPERNATURAL_LEARNING_POSSIBLE]
[IS_SECRET:MUNDANE_RESEARCH_POSSIBLE]
[IS_SECRET:MUNDANE_TEACHING_POSSIBLE]
[IS_SECRET:MUNDANE_RECORDING_POSSIBLE:objects/text/book_instruction.txt:objects/text/secret_animal.txt]
[I_TARGET:A:CREATURE]
[IT_LOCATION:CONTEXT_CREATURE]
[I_EFFECT:ADD_SYNDROME]
[IE_TARGET:A]
[IE_IMMEDIATE]
[SYNDROME]
[CE_CAN_DO_INTERACTION:START:0]
[CDI:ADV_NAME:morph into a bear]
[CDI:INTERACTION:MORPH_BEAR]
[CDI:TARGET:A:SELF_ONLY]
[CDI:WAIT_PERIOD:0] <-- No wait period; the SYN_CLASS will ensure that they cannot transform.
Or if you want it as a natural ability:
[CAN_DO_INTERACTION:MORPH_BEAR]
[CDI:ADV_NAME:morph into a bear]
[CDI:TARGET:A:SELF_ONLY]
[CDI:WAIT_PERIOD:0]
You can make as many transformations as you want this way.