I guess u cant hav a direct bus.
The nearest point would be Palayam, because the East Fort-Kochuveli bus goes Via Gen Hosp.
There are many buses from Pattom to Palayam. You will have to get down at Palayam and catch the Volvo if I am not wrong. Not sure of the timings though. Kerala SRTC doesnt seem to run its Volvos on a schedule. Sometimes they come many in an hour, some times there wont be any for hours..