The currently mandated legal minimum according to Singapore's Employment Act is 7 days for the first year and it increases by a day for each year you stay with the same company.
Details are here:
Ministry of Manpower Annual Leave
However that being said, the 'benchmark' average is 14 days for most companies but will vary depending on company/industry. Government and civil service tends to give a bit more (usually 18), private companies at the start a little less (12-14). Note that this does not include sick days.
I am not sure what you infer by buying back additional day's holiday here but it would be more like no pay leave, just basically not being paid for that day that you took leave for once you have exhausted your year's allocated leave.
By bank holidays I presume you mean public holidays here (Christmas, New Year's and such)? There are basically 10 events per year that warrant a holiday in Singapore. Generally around 20 days give or take depending on which day of the week the holiday falls on.
Again details can be found here:
Singapore Public Holidays
As an extra bit of info, the breakdown of these 10 events are divided for 3 major cultural races staying in Singapore (2 each for the Chinese, Malay and Indian), 2 Christian (Good Friday, Xmas) and 2 general (New Years, National Day).