I don't know if this applies to all wasps and bees but I can usually tell them apart from their movement, wasps tend to be jumpy, they have jittery, jerky, stop and go action when they are on the ground or perched on a flower, bees tend to have a much smoother, fluid movement.
I looked at possible species of either bees or wasps around Singapore and found 3 possible species that could be it: The White-cheeked Carpenter Bee, the Yellow-and-black Carpenter Bee or the Pubescent Carpenter Bee. I also found some similar photos under Subgenus Koptortosama which includes about 60 species of carpenter bees, the majority which had no photos. Let me know if you would like to compare the photos and I will PM you the links rather then spam a bunch of external links here.