Does anyone! understand babies?
Not sure what a bassinet is or why it would fit on a bulkhead.
The only suggestion I can make is that if they are under two your option might be to book a seat for each. Cost may be an issue but $400 for a bassinet sounds expensive, I would hope the ticket for an infant is less. You can then put your baby seat in the pax seat. If the seat isn't suitable for the airline you use then you need to use a baby belt which fits to your pax belt but you only need this whilst the seatbelt light is on. Then you can pop them straight into their car seat for the rest of the flight.
Sorry I can't be any more help than that I'm afraid.