How much in advance should we book a bullet train from Beijing to Xian on Oct. 12?

It will be very difficult to buy tickets for you, because October 1st-7th is national holidays lasting one week and many people will prolong them for few more days so all trains will be very busy before and after October holidays which are 2nd biggest holidays after Chinese New Year. I suggest you to not travel to China at this time and wait at least until 2 weeks later.

Well, we do not have a choice about when we will be there, so the question still remains, how soon do we need to book a bullet train ticket on October 12 from Beijing to Xian? Can we do it through the internet?

Book it as early as possible, especially, from Apr to Oct in China.