Ah, the great 3 year old debate...
The thing is, all 3 year olds are not created equal. I have seen some 3 year olds sit more patiently than some 5 and 6 year olds do, but I've also seen some terrible, TERRIBLE situations in which the younger ones are scared, nervous, crabby, etc....fists flying, tears flowing.
Please use your own discretion. You know your child better than anyone else, so only you can tell yourself whether or not she'll be able to sit still in the chair or imagine how she might handle it. You might try having a practice round - a couple of weeks before your appointment, play make-believe and set up a chair for your dd to sit in, and and explain that this is how things might go at bbb...comb her hair, make a ponytail, maybe even pretend to paint nails and put on makeup. How she handles it may or may not be an indication of how things will go at the actual appointment, but...you might get some idea. My advice: make sure dd is well-rested, well-fed, and is very clear on what the bbb is and what we do there! And of course, hope for the best