。
She walked out without even saying "please sit down" to me.
Literal
She [topic-は] me [to-に] sit-please [quotative-とも even] saying-not [without-ずに] left.
Three things to notice. (1) お座りください ('please sit, do please be seated') is the お+verb-stem+ください honorific request frame — used in formal hospitality, customer service, and polite invitations. Compare お入りください ('please come in'), お待ちください ('please wait'). (2) The combined particles とも ('quotative と + intensifier も') = 'as much as saying X / not even saying X' — sharper than plain と. (3) 出ていく (here as 出ていった past form) = 'go out and away' — the te-form chain combines 出る ('exit') + 行く ('go') for departure with directional movement away.