You can't (legally), and unless you go during some particularly miserable weather you may find it to be surprisingly busy. Its a small place and access is extremely easy. If you are going to camp, probably best not to light a fire because that's probably the easiest way to attract the attention of someone keen to move you on.
Last time I was there I used a campsite, South Penquite. Seemed reasonably priced to me, they allowed fires and had unmetered hot showers, Luxury! They're also only a few minutes walk from the pub in Blisland, which was excellent.
Much of the central area of the moor is farmland (sheep farming mostly but a few cattle too in summer). I've often seen farmers on quad bikes feeding sheep on the remotest areas of the moor - it is surprising how well quads cope with the roughest terrain.
Certainly there is no right to camp on Bodmin Moor. AFAIK, Dartmoor is the only substantial area in England and Wales (it's different in Scotland) where wild camping is specifically allowed - even in camping-friendly places such as the LD it is tolerated rather than allowed.
As Serriadth says, most of Bodmin Moor is easily accessible - even the centre is bisected by the A30 - and although it is criss-crossed by footpaths many are not rights of way, merely permissive paths (such as the track from Rough Tor to Brown Willy).
I would strongly advise against lighting a fire. That would certainly attract attention to you - the glow by night, the smoke by day - and would be entirely counter the 'leave nothing but footprints' approach to wildcamping.
All that said, if you seek out a really secluded spot well away from tracks and livestock and if you don't light a fire and if you pitch at dusk and strike camp at dawn, you'll probably get away with it. If the 'Beast of Bodmin' doesn't get you, of course...
It’s not all hill walking and Kendal mint cake
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