Blanche lives her entire existence in the shadow of the Daedric prince and divides her time between sitting silently on one of the benches, placing an offering in front of the shrine, or preaching from behind the lectern. When not doing any of these activities, she simply wanders around.
If you speak to her before you start the Namira's Shrine quest she will say, "Don't talk to me. Talk to the one in the robes.", referring to Hjolfrodi the Harrier, who you must speak to in order to summon Namira.