Figures — you're a lady of quality. It's not like you've been living some free-spirited life.
Literal
As-expected, honorable-young-lady. Free-and-unrestrained [copula-な] life [obj-を] doing-[-ていた] [reason-わけ] [copula-じゃない] [explanation-んだ].
さすが 'as expected / that figures' opens with affirmative recognition. お嬢様 'young lady (of high station)' with the honorific お + 様 is the standard address for someone from a wealthy/aristocratic background. 自由奔放 'free and unrestrained' is a 四字熟語 for uninhibited behavior. ~ていたわけじゃない 'it's not that one had been X-ing' negates an assumed state using わけではない. The speaker is presumably reassessing the person having learned their social background.