She's NORMAL.
This is a stage... of development. And will occur then subside and may recur per the age of the child and developmental progress.
A child professional once told me, that it is GOOD that a baby/child does this.... it is normal. BUT, if a child never does this, then THAT would be a concern and a developmental abnormality.
Do not 'force' her to be 'friendly' with people/strangers.
At this age and even in Toddlers... their emotions are not even fully developed yet... thus, you cannot expect "adult" parameters of socialization to occur, in a baby or young child.
It is good... she does this. It is Instinct. You are her Mom... and "safety" for her and bonding.
If my kids as babies did NOT want to be held or go to someone... I told that person... no.
When my kids were babies and toddlers, I never.... forced or expected them to be friendly, with people if they did not want to. I want them to develop... their own "radars" for people... good or bad.
My daughter for example, now has an astounding 'sense' of who is 'off' or unsafe or dangerous. She can tell.... and has good instincts.
Anyway, your baby is very normal, and per her age.
Her reactions... are good.
I recommend the books: "What To Expect The First Year" and, "What To Expect The Toddler Years."
DO NOT.... try to make her "popular and brave" when meeting strangers. This is the WRONG message... to teach a child.
Always go by your child's personality... AND sense of safety... per strangers too.
My Daughter, even now, will NOT talk to anyone... that she gets a 'weird' vibe from. AND she is often... correct about the person. I am... PROUD of her. I do not force my kids, to be all friendly and/or 'brave' just for strangers.
all the best,
Susan