For a much more affordable trip to Tottori, consider taking a bus.
You can reach Tottori from Osaka for only 3600 yen, which is half the amount you will pay if you go by train.
There are buses to Tottori from places as close as Okayama and as far as Tokyo and Fukuoka, with many places in-between, like Kyoto, Hiroshima, and Kobe.
There are a few ways to reach Tottori by train.
Trains that go directly to Tottori can be accessed from Kyoto to the east and from Tsuwano, Masuda, and Matsue to the West via the Limited Express trains.
Alternatively, you can first go to Okayama and then transfer to the JR Tsuyama Line. From Tsuyama, take the JR Inbi Line to Tottori.
I use JR local train special ticket (18 kippu) that availbale only during spring, summer, and winter, it is about 3 h from Okayama to Tottori. From Okayama station to Kamigori use the JR ticket, and change train to Chizu (not JR, so you have to pay 1000 yen). From Chizu use JR again to Tottori.
18 kippu can be used only for JR train. Other train from Kamigori to Chizu is not belongs to JR, it has separate train line and platform at Kamigori station.
18 kippu cost 11500 yen for 5 days or 5 peoples in 1 day. So it costs only 2300 yen per day. Available only during spring vacation (March 1st- April 10th), summer vacation (July 20th-Sept 10th), and winter vacation (Dec 10th-Jan 20th).