Bribes (as well as the negative, consequence) are excellent methods. Think of it as teaching life lessons. All things worth having (the bribe) must be earned, and all things prudent to avoid have consequence. If you tailor your method to this, it may help her, as well as your conscience.
Also, be sure not to give too much attention to negative meltdowns, as though they produce negative attention, they do result in attention. In some cases, attention is exactly what they want, at any means possible.
In the same line of thinking, don't be afraid to show (for her, as well as for yourself), that you are willing to be embarassed, lose valuable entertainment, lose shopping, etc for the purpose of correcting her behavior. If that means allowing her to tantrum in the house while you ignore her, so be it. If that means leaving the store early because she won't behave, so be it. And so on.
Remember, though she is beginning to reason, she is very literally insane (irrational). Her lack of experience and ability to relate to situations through previous knowledge will necessitate her reliance on her emotion. Though this doesn't follow in line with her desire for some independence, of course. In order to curtail improper emotional responses, you must provide situational reason. That is, negative response for incorrect behavior (consequence), and positive response for excellent behavior (reward, even if it's a verbal reward).