Hi there I arrive at Beijing airport at 0530 this Thursday 3 sep

You can take the shuttle bus line 3 to BJ railway Station (CNY24), where you can take the bullet train to Changchun. The train ride is about 6.5 hours.
Don’t worry, the shuttle bus line 3 will start operation at 05:00am.

Thanks so much Alan I didn't realise how far I have to go! can I catch a plane to Changchun instead? That's a long train ride after a 13hr flight from NZ!

Yes, of course. Right in the airport, you can take a direct flight to Changchun Longjia Airport, and the air duration is about 2 hours, which is much faster than the bullet train.

Ok cool... Can I just book the flight that morning when I arrive at the airport incase my flight delayed weather here is very bad this week..and do you know How much that will be?

Yes, you can buy the flight tickets in that morning.
But the thing is if your international flight delays, you may need to wait for a long time to take the domestic one. As the airport will not operate any departure or arrival from 09:30 to 12:30 due to the military parade.
From BJ to Changchun, the approximate flight fare is CNY 700 to 1,000.

Thank you so much for your help! I think I will have to take the bullet train is that from the BJ railway station?

Yes, you are right. Currently, the available schedules are at 06:58, 07:13, 07:30, 13:51, 14:18...
Ticket fare for a D tye is CNY 350.5 for the first class, CNY265.5 for the second class; for a G type, ticket fare is 660.5 for a first class and 433 for a second class.
You can check the details on this website.

Ok thank you how far is the airport to the train station? How far and how much by taxi? Is there only one train station? Do you think I will make it for the 7.30am train I arrive BJ at 5.30am and have to make it to Changchun and then then university

Hi there, there are four train stations in BJ and I just found out that some of them have been moved to the South Railway Station, inlcluding the one departing at 07:30.
To catch that departure, you'd better take a taxi to get to the station directly, as both airport shuttle bus and airport express are not opened yet in that early morning. Time is a little bit tight, so hurry up.
Distance between the airport and south station is about 24 miles. If by taxi, it takes about an hour and CNY 120.

Or to make it easy, you can go to BJ Railway station to take the one departing at 10:02. Distance is about 19 miles. It takes about 40 minutes and CNY100.