I bet crossing outside EU borders with a vehicle that's not your own, as cargo, is automatically a LOT more paperwork than just crossing the Single Market area. Turkey has a customs union with the EU, but I'm not sure how that affects used vehicles in this case...

Schengen is indeed not relevant, but the Single Market very much is - which is why Bulgaria, a non-Schengen country, is a practical shipping destination.

Honestly, that's not a terrible option. I just paid the same to ship my bike from Tallinn to Milan and back, but that's only because I used a specialist shipper who bundles multiple bikes, has their own transport frames, and crucially *stacks them two-high* - buying one bike's worth of space on a truck and shipping two bikes in it - so yeah, it's the same as what I paid, and I think I got a good deal compared to riding all the way myself.

I know that DSV, the very large European truck shipping company, has been used by people who crated bikes themselves. Try contacting your local DSV office and ask them for a quote - two europallets worth of space is enough for even a large bike with luggage.

EDIT: Amsterdam to Plovdiv is over 2300 kilometers and 24 hours of straight riding, let's say that's 3 days of all-highway. At 6L/100km, that's about 140-145 liters of fuel, let's say 250 euros in fuel alone. Plus 3 nights' accommodation, let's say cheap F1-style motels - another 200 euros. Plus food, road tolls, and crucially - wear on your bike, maybe a quarter of the entire life of your tires? And three days of your holiday time. Given that, 591 euros for shipping the bike and all your luggage, plus maybe another 50-100 for a Ryanair flight, is actually a really good deal.