3hrs is a long wake time for a 3mos old before bedtime. canyou post what her general day is like ie. when she usually wakes for the day, when her naps are, how long they usually are etc? she is most likely fussy at the end of the day because she's overtired and when a baby that young is overtired, the rocking/bouncing etc tends to stimulate them more making them more fussy.
don't be scared of an early bedtime - most people think that an early bedtime means an early wake but that is quite the opposite. when a tired baby goes to bed early for the night, they tend to front-load their sleep and get the much-needed rest at the beginning of the night and tend to wake up later and more rested.
i think when DD was 3mos, her bedtime moved from 8pm to 7pm to 6:30pm then to 6pm because i also noticed that she was crying a lot more and more fussy when we were putting her to bed later. i would suggest an earlier bedtime and see if you can get her in the crib by 6:30pm or even 6pm and see if that works and reduces her fussiness.
GL