Taxi from Yonago airport to Adachi

I have a flight from Tokyo to Yonago which gets in at 8:15 AM. From there I plan to go to Adachi Museum of Art. I understand that I can take a train from the airport to yasugi then take the free shuttle bus to Adachi museum of art. However, when I plan this trip out on google maps it takes a considerable amount of time. I am considering taking a Taxi from the airport to Adachi which I assume shouldn’t be a problem although it will be fairly expensive ~ 13,000 yen (it is for two people). The taxi could save me anywhere between 1-2 hours of travel though. Google maps doesn’t show taxi as an option, but it may be because google maps doesn’t understand how to get to Adachi at all … for example if you ask for directions from Yonago to Adachi it tells you it can’t find any routes. After I visit Adachi I am taking the train to Okayama and was hoping to see Korakuen before it closes so saving an hour or two is worth it. I assume it will be easy to find a taxi stand at Yonago. Is there any chance the driver would refuse to drive to Adachi? It is a 30km trip.

Taxi is the best.
But you can go by public transportation.

According to the taxi website, it was about 10,820 yen (about 60 minutes). https://www.taxisite.com/far/anytoanyret.aspx?departure=35.502321%2C13...
It is better to book a taxi in advance.
https://www.yonago-air.com/access/taxi
Hinomaru Hire Contact Form
https://www.hinomaru-hire.com/contact/yonago/
Yonago Daiichi Kotsu has an E-mail address.
http://yonago.0152.jp/