Cwatters,
I can only speak for BA,we have ample bassinette seats on L/haul aircraft.
747s have: 2 in First
6 or 10 in Club(dependant on config)
8 in economy
777s have: 2 in First
4 in Club
2 or 6 in economy(dependant on config)
We will provide you free of charge our own "Britax" designed adjustable seat or cot...or both if you see fit,which the crew will attach to the bassinette table in front of you.The seat adjusts from a sitting position to a relaxing lie down position which you can easily do yourself.If,when baby wants to sleep,and you would prefer a flat cot,the crew will happily switch it over for you.
You can of course bring your own car seat,but it has to be CAA approved as opposed to FAA,but basically as long as the seatbelt will fit underneath the car seat and attach to the aircraft seat and be facing forward(cannot be put on bassinette tables)then no problems.I guess this would mean paying for a seat though as opposed to paying 10% for infants and using the bassinettes.
Have had many pax over the years travelling with two babies and have never had any problems.Bassinettes seats can be pre-booked when travelling with babies.
We carry enough of each on board to satisfy every position and have never been on a flight when there have been more babies than cots.
Have been on flights though,when pax have had to have babies on laps for entire time when bassinette positions have been occupied by people without babies,due to either the pax not pre-booking,or by then arriving so late at airport that bassinette positions are then allocated to other pax.I believe they are held by check-in staff until very late on incase people arrive with babies and have not pre-booked.
Hope this helps.