Which ship, as The RainForest Room is not the same on all the ships.
Yes you can do a day pass, the price is around $30 depending on the ship and cruise.
You have to go on the day you want to go, it can not be booked in advance.
They will give you a sticker for your KTTW card and you will hand in your card during the check in process. They will give you a wristband similar to the Magicband which will unlock the RainForest Room door.
You can stay as long as you like and you can go in and out multiple times during the day.
The rooms are small and can get busy, so I usually go early morning or on port days. Sea days are peak times and they might not do day passes depending on how many length of cruise passes they have sold.