Can anyone please suggest schools in Singapore with good bilingual programmes in english & mandarin?

I think ur consideration is valid for preschools but invalid for primary school. Maybe it's fair to judge preschools and the number of years spent there is shorter as compared to primary school and it is easier to change preschools - teachers come and go and in preschools is actually v flexible. For primary school - every school is a good school - especially language which is extremely fundamental. There is no use recommending because teachers get transferred every now and then