Allow us to expand the question to deal with a variety of related cases.
Chazal forbade hatmana of food on Shabbat out of concern that while insulating food to retain its heat, one might heat the food in a manner that violates Shabbat.[1] It is forbidden to do hatmana even before Shabbat into a medium where heat is being added to the system (mosif hevel).[2] Thus, if placing the cooking bag inside the chulent is considered hatmana, it is forbidden. However, usually there is either no issue of hatmana, or it can be easily avoided.
Firstly, it should be clear that cooking one food directly in another is not hatmana. The issue of hatmana arises when a food is not being cooked with the rest of the pot but is placed in it to become or remain hot, as a separate unit. Even this is a problem only when it is separated from the rest of the food by a utensil or at least a significant covering.[3]
Putting cooking bags in a pot of a boiling liquid is considered a manner of cooking, not of hatmana, and is therefore permitted.[4] If one intends to mix the tastes of the different foods by heating them together, even if they were previously cooked (e.g., matzo balls in soup), then this is considered cooking together and permitted. The fact that one or more of the foods is in a bag is not a problem, especially if that is done to prevent the food from falling apart or diffusing. Using a porous bag or making holes in the bag are indications of the desire to have the foods interact.[5]
Even when none of these criteria are met, we pasken that hatmana applies only when the food is insulated on all sides.[6] Therefore, one may warm a securely wrapped kugel that was baked separately by placing it in the chulent pot before Shabbat if a reasonable portion of the kugel protrudes above the surface of the chulent.