I used a beach very close, well 1 to 1 1/2 miles to the west, called Cogden about a mile east of West Bexington a couple of years ago when we were on holiday at Westbay.

Didn't realise Burton Hive was naturist.

Revisiting photos I took during my Westbay holiday in 2009 I now realise that Cogden is west of West Bexington (about a mile) not east which was another spot I used briefly. Sorry for any confusion I may have caused.

Hive Beach is very nice but is always busy during the summer months. There is a cafe, toilets and shop there though.
NUFF says says it is naturist to the East but when I went several years ago and stripped off - about mid morning - the beach slowly filled up with textiles. You have to go even further to the east and then you end up at Cogden Beach anyway.
There is a separate carpark for Cogden Beach. The beach is quieter and used mainly by beach fishermen. If you walk towards the East when you get to this beach you can find plenty of space for naturising. Virtually no walkers along this stretch.
Back at Hive beach, I have walked to the West away from the crowds and stripped off there. Other naturists often there as well. The beach is not very deep and there is often passing textile traffic.
I have not been to either of these beaches for a while.
Pic of the area from the cliff

Is this the section of beach you used ?

Only asking 'cos the photo looks to me likes it's taken on top of East Cliff next to Westbay looking over Burton Freshwater beach adjacent to the very large caravan/ holiday complex to the similar cliff formation which saw a collapse leading to a fatality earlier this year.
Burton Hives as I remember it is around this headland out of site & stretches around another headland (with a caravan park on top) before merging with Cogden.

Having said that I was on holiday only once in this area a few years back & stand to be corrected.

You are right furrysqueeze , it is from the east cliff by West Bay with Hive Beach around the headland.
The spot I used was about halfway between the Hive beach car park and the caravan park that is nicely out of view in the picture. The beach there is narrower than the one in the picture.
From my archives the picture was taken in 2003!

From my re-collection Burton Hives has something resembling sand, while Cogden is a huge bank of stones, although this might have been due to the state of the tide, and Westbay had a semi-sand shingle.

I would not describe Cogden as a huge bank of stone. See attached pic from 2004. This was taken in August according to the file properties. As you see nice and quiet - though maybe too quiet for some.

Taken at the back of the beach on the coast path, it gets a lot more stony & rougher by the sea - and drops down steeply.

Update: Not Hive beach but Cogden Beach a little to the east. Lets start at the car park that is quite small but doesn't really get to busy during the week but is packed out at the weekend. Parking is 40p for an hour £1 for up to 3 hours & £2 for all day!
Now the beach is comprised of small pebble's there quite comfortable to sit on if you take a little effort to smooth to your area. If you walk from the car park for about 10 minutes in easterly direction you'll find yourself in front of Burton Mere That's the GPS coordinates 50.688409, -2.699925 You'll find yourself's at the acceptable area for public naturism. In our opinion this is one of Dorset's best kept secret's you may on a busy day run into a couple of other naturists which is a shame because if you realised how great this location is you'd all be there. The only downside is the steeply shelving beach which if you feel like venturing into the water is frighteningly cold. Also anything other than a flat sea you may want to avoid getting into the water above your knee's. Other than that small fault we cannot recommend Cogden Beach enough ! The only other thing we can think of is without a good breeze you get to feel so hot because those pebble's retain a lot of heat ! And if your a big jessie like me you won't go into the water too cool down. But if your hardcore like my Portland born & bred wife it's like bath water  ;D

I take it the car park you refer to is the National Trust one which runs down the hill from the main coast road opposite Cogden Farm, the bit I used a few years back was just beyond the east end of Burton Mere which is directly below 'Othona' on the coast road, the sea wasn't cold but I'm from North devon, although I found the undertow of the receding waves caused by the steepness of the shore a bit disconcerting after the gently shelving sandy experience of Saunton, but prepared me for using Ringstead Bay a couple of years later.