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I think she's showing off her new dress to us.
Literal
She [topic-は] us [to-に] new dress [object-を] is-showing-off [quotative-と] think.
見せびらかす ('to show off, to flaunt') is a richer verb than plain 見せる ('show') — it adds the connotation of doing so deliberately for attention or admiration, often with a hint of mild disapproval. The ~ている marks an ongoing demonstration; the ~と思う ('I think that...') hedges the speaker's claim, framing it as their interpretation rather than fact. ドレス is a katakana loanword, typically referring to a Western-style dress for formal or special occasions — for everyday clothing, ワンピース or 服 are more common.