There are several options from New Town Plaza to Central, however, none of them are directly connecting the two locations since planners expected passengers to take the KCR.
The first one would be KCR to Kowloon Tong and transfer to MTR. With the opening of the new Tsim Sha Tsui extension later this year, KCR passengers will soon able to transfer to MTR in Tsim Sha Tsui or (if you don't mind a little walking) Star Ferry. There is also another cheapest and fastest way if the there isn't any traffic in the tunnel. You can take the KCR to Hung Hom and transfer to bus routes such as 101, 103, 104, 109, 111, 113, 115, and 182.
You can also take 170 that goes to Aberdeen but you still have to transfer to other bus routes (2, 5B, 10, 11, 25, 26), tram or MTR in Causeway Bay near Times Square.
170+2 or 26=$15.3+$3.9=$19.2
170+5B or 10=$15.3+$3.4=$18.7
If you live in other parts of Shatin such as in City One, Tai Wai, or Ma On Shan, you will have direct bus routes to Central such as 182, 680, 681. To connect to one of these routes, the shortest you can take is 284 from New Town Plaza Bus Terminal or 86K from Shatin KCR Station and get down at one of the stops along Tai Chung Kiu Road where you can transfer to 182, which goes to Sheung Wan via Central.
Hm...all the bus routes mentioned are frequent. It just requires a little investigation and trial and you will be prepared if there is something wrong with the KCR or MTR...