This is one of the rare cases where English uses a subjunctive tense.
It is mostly used in American English after certain verbs like request, advise, ask, beg, decide, decree, desire, dictate, insist, intend, move, order, petition, propose, recommend, request, require, resolve, suggest, urge, and vote.
NO,SHE REQUESTED THAT ``I NOT BRING´´ ......present subjunctive
NO,SHE REQUESTED THAT ``I DON'T BRING´´ .....normal present tense is sometimes used instead
NO,SHE REQUESTED THAT ``I SHOULD NOT BRING´´ .......in British English 'should' often replaces the subjunctive.
NO,SHE REQUESTED ME "NOT TO BRING".......sometimes the infintive is used instead
present subjunctive of the verb bring,
He bring....no s
There is also a past subjunctive in English. Here is a good reference: