All day. Public transport from UNSW to Central isn't exclusive for UNSW. There are people who live in Kensington.
391, 393, 394, 396, 397, 399, L94, M10 all go past on Anzac Parade iirc.
M50 and 891 (express) and 370 (Only from Green Square though) go past on High street.
There are a lot of public buses which go past UNSW. If you are absolutely unsure just ask the bus driver.
372, 374, 376 (from Central) and 373 and 377 (from Museum) go to the Racecourse and Randwick campus if you ever need to go past there.