Airport Express to HongKong station, Central. Check the time table here http://www.mtr.com.hk/eng/train/ae_timetable_e.htm , don’t miss the last train at 00:48. Then get a cab to Stanley should take 30 minutes or less in the mid-night normally.
Woodleigh house is very close to the Stanley bus terminus. Within 5min walking and just opposite to the Stanley police station, which is right next to the bus terminus.
There are quite a lot of bus routes from Central to Stanley, but most of them stop running around 19:00 – 21:00. Only route #6, from Exchange square (Central near the HK station) to Stanley up to 1:00am; and if you arrive on Sat, Sun or HK public holiday, #N6 runs overnight. In the mid-night, it should take 40-50min.
As a newbie of the city and you might have bags with you, I think you better get a taxi from Central.