。
She loved talking about herself.
Literal
She [topic-は] own story [object-を] do [nominalizer-の] [subject-が] loved.
自分の話をする ('to talk about oneself, to tell one's own story') is the standard way to phrase 'go on about oneself' — context decides whether this reads as endearing storytelling or self-absorption. The nominalizer の packages the verb phrase into a noun-like unit so it can take ~が好き. こと would also be grammatical here; の typically sounds slightly more concrete or experiential, while こと leans toward general/abstract statement.