The Interfax news agency initially reported her arrest on Sunday night, but later said she was on the run while her mother and sister were called in for questioning. The Interior Ministry placed Ms. Tryopova on its wanted list on Monday.
Witnesses said the suspect had asked questions and exchanged comments with Mr Tatarsky prior to the explosion.
A witness, Alisa Smotrova, said the woman had told Tatarsky that she had made a bust of him, but that guards had asked her to leave it at the door, thinking it might be a bomb.
They joked and laughed, and then she went to the door, picked up the bust and presented it to Mr. Tatarsky.
A video showed Mr. Tatarsky joking about the bust and placing it on the table next to him just before the explosion.
No one has publicly claimed responsibility for the attack, but military bloggers and patriotic commentators immediately blamed Ukraine, comparing the bombing to that of last August. murder of nationalist TV commentator Darya Dugina.
Mrs. Dugine was killed when a remote-controlled explosive device was planted in her SUV exploded while driving on the outskirts of Moscow.