Georgia is fantastic. Possibly, one of my favourite countries to visit.
First travelled there in 2014 while doing a loop through from Wales through Turkey and Georgia to Moscow and back through Latvia, Lithuiania and Polan back home.
Back then you couldn't get insurance for Georgia not even at the border. But it didn't matter because they couldn't care less!
That trip was on XT660's.
No visa required for Georgia, Turkish e-visa was easy (get it online).
Food and people were just great.
The Georgian military road to Russia was fantastic. It had only just been rpaired after land slides had destroyed it.
https://old.civil.ge/eng/article.php?id=27240
It was swept away again shortly after we used it.
https://old.civil.ge/eng/article.php?id=27596
Next visit was on the way to Azerbaijan on R1100gs. Stopped in Tblisi on the way there and again on the way back. Me and Simon had a day trip to Armenia on the way back sans luggage while we were staying in Tblisi.
This time it was still difficult to buy insurance and they did want to see it. But easy enough to buy at the border.
I can definitely recommend a visit and I dearly hope we can go again.
Not sure why you need to ship a bike out though. Just ride the thing. You can get to Turkey in 3 days.
Turkey itself is a great country to visit.