hey. I'm from Kelowna, skied at big white since i was three years old, and went to UBCO for two years.
The mountain is 45-60 mins away (Silverstar is 60ish)
As you said, Big White shuttle bus leaves UBCO campus at 7:45. There are multiple busses that do pickups throughout Kelowna (incase you don't live on campus). You need to buy the bus pass with your seasons pass if you want to take the bus (it's 21$ a pop otherwise).
The is the "UBCO Mountain Riders" club (kind of a joke), and they don't organize rides, but it's fairly easy to hitch up there with people. I would recommend buying a bus pass though.
Anything else about Kelowna/Big White/ UBCO pm me.