There are bus services from Parramatta Interchange to Bankstown, all run by Veolia.
907 - 52 minutes
909 - 53 minutes
910 - 58 minutes
From Parramatta Interchange to UWS, a variety of services run, as seen in
this document, as well as
this.
Sydney Buses
520,
521,
523,
524,
525.
These services are quite frequent during weekday business hours, and is about an 8-10 minute bus trip.
Also, Bankstown train to Lidcombe? Won't you have to change at Sefton or something?