<font face="Verdana, Arial, Helvetica, sans-serif" size="2">Originally posted by MilesDependent:
I wanted to get a bus, but I was told that the bus stops running at 9:30pm.</font>
There could be some miscommunication here. There are several bus companies which run buses to/from TPE airport. I know Airbus runs until 2AM to Hyatt, among others.
It is possible that buses to Westin stop running at 9:30pm, but there are other buses to Taipei city available and Westin could be just another short taxi ride away (no more than NT$100). Hope this helps for your future trips.