Bus from Beijing to Jiayuguan

Hi, I'm afraid there is no direct long-distance bus from Beijing to Jiayuguan. Thus I suggest you take a train at Beijing West Railway Station to Lanzhou first. Then you can transfer to another direct train at Lanzhou to Jiayuguan. Compare with the direct train from Beijing to Jiayuguan, the transport transference Beijing-Lanzhou-Jiayuguan almost takes the same time.
And if you wanna book a ticket in advance in case of selling out again, this website is provided for your reference.
https://www.travelchinaguide.com/china-trains/
Hope it help. Good Luck!