As far as I know, you still have to pay for seat selection.

If not, I'm going to start claiming I have a baby, getting a free infant ticket on domestic flights, and getting the bulkhead for free, then claiming the baby was too sick to fly.

Here's how the process works: Book your fam into bulkhead seats that show the bassinet icon in the seat maps, consider a comfort fare since it includes preferred seats. Call in to add the infant and request the bassinet. Hopefully the flight attendants will approach you after takeoff and install it. Enjoy the flight.