Hmmm...not easy on a Sunday I'm afraid. Don't think there are any buses on a Sunday through Silverstone.
The best way is by train to Northampton, bus to Towcester then a taxi to Silverstone. Even then you'd probably not get there until lunchtime missing the morning action.
Hiring a car might be an easier option (if you can!)
Well worth it if you can make it. BTCC is excellent entertainment. Was at Rockingham at the last round and it was superb.
And wrap up warm if you do go...those grandstands at Silverstone feel pretty bleak in late September.
Love it though...I'm hoping to be there!
For future reference, Rockingham is probably the easiest circuit to get to for public transport. Corby train station looks like it's only a mile or two away from the circuit. Easily walkable if you're up for it!