Some kids are outgoing. Others, not so much. Some get scared by facial hair. Some get scared when it goes away. I can't say for sure why your niece is nervous around you, but I can take a guess.
Most likely, she just isn't familiar with you. She sees grandma pretty often and isn't scared of her. She's seen grandma be nice and loving. I'd also wager that mom and dad were close by when she met grandma. She probably gets nervous because you are new, she doesn't know what to do and mom and dad aren't around to let her know things are ok.
First, I would try to spend more time with her and your brother and his girlfriend. If she knows mom and dad are there, she should feel more safe and can get to know you a bit better without being scared. Play with her with her parents. Do things with her and her parents together until she gets used to the idea of you being around. Then try doing things with less parent interaction. Play all together then have mom or dad or both stop playing. They could be in the same room or leave entirely. Eventually she will warm up to you.