It’s odd how something as enormous as a 2-ton white rhino can sneak up on you unnoticed.

During our bush walk at Thanda Safari, a big five private game reserve in KwaZulu-Natal we become engrossed by a lion, a beast with a glorious mane, prowling on a plain. The lion could cover the ground between us in four seconds, Thanda’s head guide Morné Hamlyn warns; but we aren’t posing a threat, and he’s fat and happy after gorging on a wildebeest for supper.

Then a rhino emerges from the bushes, heading straight for us at a rapid trot. We gasp, swear, and tremble in awe and fear as Hamlyn yells at our tracker to lead us into the thicket. He strides forward confidently, smacking his hand against the butt of his rifle, yelling and pacing towards it like a man enraged.

He looks a little like a lion, with his ginger beard and sizeable stature, and the startled rhino turns away. Then he remembers the real lion and decides our direction is safer.

Hamlyn is yelling, slapping and gesticulating at the tank of a rhino now only 12m away and moving with the deadly inevitability of a bowling ball heading for skittles. As we back away rapidly I wonder which one of us will be hit first.

At the last moment Hamlyn’s unrelenting ferocity spooks the rhino into pelting off across the plain. But the adrenaline rush isn’t over. The bemused lion has swaggered over to investigate the commotion, and when I glance over my shoulder I see it stalking us. “Don’t worry about what’s behind you,” Hamlyn growls as he falls in at the back.

We set a cracking pace through tall grass, with pounding hearts, dry mouths and sweaty palms. Eventually we stop and look at each other with wide eyes, and laugh with sheer relief.

Bush walks are normally sedate affairs to admire the plants, trees and insects, and Hamlyn later describes this as one of his top five experiences in 18 years. It reminds us that wildlife is called wild for a reason, and leaves us tingling with life and more in awe of the animals we usually only admire from the elevated safety of a vehicle.

The next morning we go tracking rhinos with the monitoring team that Thanda set up two years ago to act as extra eyes to its antipoaching unit.

After examining footprints and watching rhino-riding oxpecker birds darting above a thicket, rhino monitor Daniel MacDonald leads us in to gaze at four slumbering giants.

Thanda is six hours from Johannesburg down the N2 and impresses with the way it encourages guests to get involved with conservation and interact with three neighbouring Zulu communities.

It is owned by businessman Dan Olofsson, Sweden’s largest private investor in SA, and he realises that visitors want to learn more about the culture they are visiting. Not only foreign visitors, since a new 40% discount for Sadc residents is making it more affordable for locals.

Guests can pay to join the conservation team for a day to help with tasks such as game counts and fence checking, or accompany the rhino monitors and perhaps watch an ear-notching and dehorning experience. MacDonald isn’t a great fan of dehorning, but adjacent reserves have done it and Thanda doesn’t want its rhinos to be more of a target for poachers than they already are.

It’s probably the only reserve in the country with a resident photographer, and guests can join Christian Sperka in his specially adapted Land Rover with Wi-Fi and a kneeling space for lower angle photography, or book a free 90-minute photography lesson.

You can also visit a Zulu community where most of the 182 employees are drawn from and meet the sangoma and her family.

Often the villagers come to sing and dance at Thanda. These cultural displays sometimes feel awfully twee, but one night as we dine in the bush, young villagers perform the most exhilarating dancing I’ve ever seen. The drums beat faster as each man shows off his dancing skills, and sand flies into my lap as they stomp the ground, in danger of scorching their fluffy leg decorations as they leap and roll close to the blazing bonfire.

Accommodation includes the Tented Camp, where 15 canvas structures boast wooden floors and posh bathrooms. After two days there we move to the Safari Lodge, which has nine enormous suites plus a spa with a sauna and outdoor Jacuzzi.

I skip a game drive for the pleasure of enjoying my private heated plunge pool, knowing that nothing is going to beat my close encounter with a lion and rhino anyway.

• Stones was a guest of Thanda Safari