From a nanny's point of view.....
With my charge, I usually have no problem putting T down for a nap, no fuss etc. Mom and dad on the other hand have a hard time getting T to go down easily. They don't use the BW methods
Does your nanny know how you are puting LO down? Does she do exactly the same? It will probably just take a little while because baby is used to you, but I am sure she will adapt well. Support the nanny so she doesn't feel like she is failing because the baby will pick up on this and probably take even longer to settle. Maybe you can just step outside/downstairs etc for a bit so nanny doesn't feel she is being watched? You can go back in a few minutes Also, have nanny take over with baby about 20 minutes before nap wind down routine starts. I know T has always kicked up a huge fuss (and still does) if he suddenly changed arms right before nap/bed. Give them some playtime together.
HTH
Sarah