General Antonyms:
* Bold
* Assertive
* Confident
* Outspoken
* Uninhibited
* Flamboyant
* Brash
* Audacious
* Forward
* Unashamed
More Specific Antonyms:
* Flirtatious (if referring to a shy, reserved demeanor)
* Provocative (if referring to a modest, restrained appearance)
* Seductive (if referring to a shy, retiring manner)
* Unladylike (if referring to a demure, proper behavior)
The best antonym for "demure" will depend on the context of its use.