You want to tour a foreing country for several weeks.
Option A: transport your own bike. Cost of transportation may easily exceed cost of the bike. Unfeasible unless you have sentimental ties with your bike and the trip must have to be done with your bike.
Option C: Rent a bike. Pros: easy to do, insurance included, well looked after. Cons: expensive in the long run, probably has to drop it where you rented it -therefore no coast-to-coast trip unless you plan to do the return trip too.
Option C: Buy a bike at the starting point. Get you one know for its reliability, and for a cross-country trip, nothing less than 750 cc. Windshield is a plus, as well as range. What about a modern Honda Nighthawk? It is cheap when you buy it new, so it must be cheaper if it is secondhand. You can get one for $2000, run the crap out of it, and at the end of your trip, pay a couple of visits to motorcycle dealers and offer them the bike for $1000. It will be well below the market price, so they just have to hand you a grand and then spend some time selling it to make a several hundred bucks profit. Win-win situation at its best.
Chances are that, after the trip is finished, you will feel "connected" to the bike and will think about taking it back home.