If you're going by public transport, I think the quickest way is to get a train to Lindfield and then from there a bus to Kuringai. If you needed to, you could probably also catch the bus from Chatswood.
Shorelink buses have a bit of a reputation for being unreliable (late), so I'd say take the train where you can, seeing as they're on time now around 90%+ because Cityrail is shaping up.
If you're more concerned about costs rather than punctuality, look up the fare saver at http://www.shorelink.com.au/ and click the right hand arrow to drop down and select "FareSaver" to read about it, it could save you quite a bit of money.
The info on the website is pretty limited (http://www.uts.edu.au/about/mapsdirections/shuttle.html), but I know for a fact that there is a more detailed shuttle bus timetable in the UTS Union Diary (free for all students in the beginning of the year).