Hi, we´re thinking of doing North, Central & South America with my girlfriend, but because we´re unable to get as long holiday as we´d want at the moment, we decided to split it into two parts. About 1,5 months in the US & Canada later this year, and then hopefully at least twice that for Centroamerica & South in 2010. Not perfect I know, but unfortunately I´m not in a position to just quit my job and go.
Shipping (by sea) actually isnt as expensive as one might think, but its slow, and involves a certain amount of hassle including the paperwork, crating the bike, etc. But I dont think flying into a country, that you´re not very familiar with, buying a bike there, handling the associated paperwork to get it legally registered in your name, and doing the trip with it, will be hassle-free, either. Even if bikes in general are dirt-cheap in the US (but do note, that they may not be nearly as cheap in other parts of America).
Not saying it isn´t do-able, and has been done by many, too, but it is likely to take some time, before you can hit the road. And we are already short on time. So for us, it´s starting to look like we will ship our own bike to America, twice, and most probably by sea. For shipping, I´m budgeting about 400 euros one way between Europe and USA, could get it even a bit cheaper I think, if I find the right company to ship with. By air it would be at least double, maybe triple that.
A plus that comes from this decision will naturally be, that we know the bike we´ll be travelling with 100%, because we´ve owned it since new, and it´s already fully equipped for two-up travelling. For us, that could well be another hassle, if buying from there - we will most certainly need a full set of panniers, etc. If you travel 1-up, most bikes will be more or less ready to go in stock form, just get a tank bag and you´ll at least have the back seat to put the stuff on.
We can get all of the bike´s necessary documents sorted out, and find out about the availability of service&spare parts for this bike in the countries we´ll plan to travel to (and even get some of the most critical spares with us if we decide to do so). And do all this before leaving home, so they won´t eat up our time during the trip.
If you got more time than us, then sure buying and selling afterwards might be a good option, too. If I had, like, a year to do this, I would probably fly to the US, and buy from there.