To spend a night in the Bungle Bungles, camping is your only option.
For independent campers, Purnululu National Park has two public campgrounds.
If camping isn't your thing, you can compromise by booking into one of the safari style luxury tents in the permanent tented camps in Purnululu through one of the tour operators.
And last but not least you can stay not in but near Purnululu National Park and just do a day trip. The nearest campground for that is on the highway turn off to Purnululu, 52 km from the park entrance.
I don't think one day in the Bungles is anywhere near enough, especially once you consider the time it takes to get there and back and even more so the time it takes to drive around inside the park. 52 km may not sound like much, but do keep in mind that the access road is an unsealed track with many steep corners and creek crossings!
I hope you have more than just one day for the Bungles, so here are your options for camping inside Purnululu National Park.
Purnululu National Park is divided into two parts, a northern and a southern area. Both areas feature several walks (see next page) and both areas have their own campground:
Those two campgrounds are very similar.
The Walardi camping area is separated into a generator and a quiet area. The generator area is also utilised by tour groups. Since the helicopter flights are starting and landing so close to Walardi, even the quiet area ends up rather noisy during peak season.
However, being so close to the helicopter flights and close to the beehive domes and Cathedral Gorge has its advantages if you are in a rush.
The Kurrajong camping area has three separate areas: quiet, generators allowed (used by individual travellers and tour groups) and an area for tour groups only.
Kurrajong is near the Echidna Chasm and Mini Palms gorge walks. It also has its own sunset lookout. (Just follow the tour groups...)
The facilities at both campgrounds are very basic: bush toilets and bore water taps. There are no showers and it is not recommended that you drink the bore water unless you boil or treat it! It's best to bring enough drinking water with you.
Fires are not allowed any more (since 2015).
You can do so here
The camping fee is $13 per person per night as of 2017. You pay your fee at the Visitor Centre upon entering the park, but during peak season you must also book online at least 48 hours ahead!
You don't have to rough it when visiting the Bungle Bungles. Bellburn—the commercial campground in the southern part of the Bungles—is as luxurious as you could hope.
The Bellburn camping facilities are located not far from the Bellburn airstrip and helicopter booking office/landing pad.
The upmarket travel company APT operates luxury wilderness camps throughout the Kimberley under the name Kimberley Wilderness Adventures. Their Bungle Bungle Wilderness Camp is located at Bellburn Creek.
The other operator is East Kimberley Tours, one of the longest standing and most established operators in the region. (And one that repeatedly got the thumbs up from Destination Kimberley readers.)
Both offer safari style tented camps, hot showers, crisp linnen, delicious meals (and stiff prices).
You don't necessarily have to join one of their tours, but you do have to book ahead to stay at one of the Bellburn camps. If you did book to stay at Bellburn, you still need to call into the Purnululu National park visitor centre upon arrival, to register and pay your park entrance fee.
If you don't need to spend a night inside the Bungles, you can also stay at the new caravan park at the Bungles access track turn-off. The safari style tents there are at least as luxurious as those at Bellburn.
Bungle Bungles National Park main page