It would take a little while to walk from WCA's house to the General. 5-10 minutes I would have thought (depending on where bus stop is). The bus would need to go down Winc road which can be quite busy and road works are scheduled to start any day now on the 2 mini roundabouts at Hill lane, allow for another 15-20mins.
Southampton is actually quite big with alot of traffic lights.
You could always park at the Cowherds pub (for free) in the middle of the common and walk up. If it's a nice day it will be quite a nice walk and I think take 15-20mins to the main campus. It's also just off the avenue so you should be able to find it easy enough.