We flew on Thai and as far as I know there are no bassinets in First at all - my son was 18 months when we flew, so he wouldn't have fit in it anyway. I believe there are bassinets in Business and generally they're allocated at check in to the youngest infants on the flight - this applies across all classes.Thanks JCB12. Very helpful. Did they offer you a bassinet for the Baby at all? O/H is freaking out about the baby being on the lap for 24 hours and thinks economy would offer a bassinet option.
You'd have to check the seat maps for each airline to see what bassinets are available in which cabins.