I did the buy and sell thing for 2 months for a New Zealand trip. Cheapest way to go for sure, but it takes time out of your trip. Took me 2-3 days to buy and another 2-3 days to sell it. You need to make sure you have a good market for selling it or else you'll be hooped.
If you can buy ahead of your trip this will help. Perhaps also try to sell it ahead too.
But its just more logistics to deal with.
Best thing is to steal a bike when you get there, then just dump it when you are done.