Yo, I lived in Thailand for 8 years.
Don't camp there. seriously, it's an incredibly stupid idea. That said, the rest of your idea might be doable.
so for motorbikes, you'll want something small and durable enough to get you anywhere. I recommend something like a CBR 150, which you can get in Thailand pretty cheap- it has good enough gas mileage and stamina to get you wherever you need to go. if you look around you can probably find one for less than a thousand dollars, but not much less. one strategy here is to find classified ads of foreigners moving back to their own countries and arrange to get one from somebody who's leaving after you get there. they need the cash and need to get rid of the thing, so you can usually catch a deal.
in terms of transport, there are some issues. Thailand has good infrastructure, as do Malaysia and The Philippines and Indonesia, but Burma has active conflicts that are still going on. Go see it if you must, but be prepared to pay through the nose for things you'll be happier not doing. Laos is much better than it has been, historically, but it's still not well developed. Cambodia is better off, but not to the point Thailand is. Vietnam is better developed than Thailand in some ways, but is not geared towards accomodating foreigners.
If I were going to do this, I'd take the motorbike around Vietnam, Cambodia, Thailand, Malaysia, and Singapore. I'd skip Burma- lovely people, but just not enough infrastructure and too much corruption- and I'd think twice about laos. This is the part where you need to do some legwork and find out about shipping a motorbike between Singapore and Indonesia or The Philippines, and I don't think it will be as cheap as selling your motorbike and buying a new one in the new country, but- because of diminishing returns- I think you'll be better off just touring around those countries the way the locals do, by bus and ferry.
as far as "living Cheaply" goes, I was stil able to find apartments for rent for 60 USD a month or so when I left in October last year (this was in Chiang Mai). So the cheapest way you'd get to see all the countries, I think, would be to find some 'base of operations' and rent an apartment there and then visit the surrounding countries from that location. on top of everything else, that will give you a place to get your laundry done and get some sleep before moving on to the next adventure. have one base in Thailand (I recommend Hua Hin, it's smaller than Bangkok and Chiang Mai, not full of criminals like Pattaya, and it's in a good middle location) and visit Cambodia, Laos, and Burma from there- the routes will take you through the major places to see (Chiang Mai, Chiang Rai, Taichilek/Mae Sai, Ayutthaya, etc) and then you can get a ferry down past the mess in southern thailand (long story, short version is muslim insurrection in three southernmost provinces, just stay the **** away) into Malaysia, and you can go all the way to singapore from there.
Then uproot, go to the next base of operations, and see the next handful of countries.