Can a Singaporean citizen single buy another 2-bedroom unit directly from HDB if they have already bought and stayed in a 2-bedroom unit before

Yes, it is possible as long as you have not exceeded your two-time purchase limit from HDB, and you meet all of HDB’s other eligibility conditions. In particular, you must have fulfilled the five-year occupation requirement of your first flat and ensure you do not currently own or have disposed of any private property within the stipulated period.