There is only one Bako option and that's the park cafe. It serves the usual, greasy noodles and stale rice. The prices are okay but you really have no choice, so you'll just have to lump it.
It's possible to barbecue but only within some areas as some of Bako is prone to bushfires; please, please notify the park if you intend on starting a barbecue as you don't want to be that person who burns down the best national park in Sarawak.
Many come laden with food, and the accommodation does provide a shared fridge so your food will be spared the 35 degree heat. Think twice about bringing pork as there are often locals staying who are Muslim and this may make them feel uncomfortable about using the shared facilities.