Dr. Barlow is a scientist so important that the Leviathan picks her up in the middle of London, and she's not going to let anyone forget it. She's also on a secret mission to the Ottoman Empire, a mission that involves some mysterious eggs she's very keen to keep safe. Dr. Barlow is a straightforward, no nonsense professional Darwinist, which is appropriate since her grandfather was Darwin himself.
We see a lot of Dr. Barlow because she takes a shine to Deryn and enlists her services as a sort of personal assistant. While Dr. Barlow can be single-minded about her work, she's also compassionate and brave.
So when the Leviathan must send a hostage in exchange for Count Volger, she volunteers; and when she discovers Deryn's big secret—that she's not yet sixteen—she keeps mum about it. When she discovers Alek's even bigger secret—his true identity—very early on because she did not fall off the potato truck yesterday, she doesn't say a word. We also know she's capable of love and affection because she loves her pet, Tazza, a lot.
In her final encounter with Alek in the novel, she says, "'Trust me, Alek'" (41.43). Despite her bossiness and her tendency to plow through everyone else with her own plans, we think it's safe to trust Dr. Barlow.