Currently, bus connections between the east (ie. Bedok, Tampines and Pasir Ris) and the north (ie. Yishun and Woodlands) is by SBST services 39, 168 and Tibs service 969.
However, bus connection between Bedok and Yishun is by Tibs service 854, which does not ply along any expressway, and result in a longer time to reach the terminating point.
When the bridge linking Woodlands Ave 7 and Sembawang Way is completed, a new Tibs service 968 could be introduced to ply between Woodlands and Bedok via the expressways, to have a faster connection between Yishun and Bedok, and to serve Sembawang passengers going to Bedok.
Route: Woodlands Ave 7, Sembawang Way, Canberra Link, Yishun Ave 2, Lentor Ave, SLE (Express), TPE (Express), Tampines Ave 10 (Express), Bedok North Rd and Bedok North Ave 1.
Although Tampines Ave 10 is mentioned, but the service ply express along that road, and also that road is at the edge of Tampines, so the service only serve one SBST territory

Bedok.
And I hope PTC will allow the service (if become a reality) to serve one extra Tibs territory (ie. Sembawang).