Fairly new owner but I seem to have bonded fairly well with my chin, Garrus. I've also have experience with older, rescue pets.
Keep in mind is that Pika is an older pet. She is set in her ways and was familiar with the surroundings she was in. I don't know her story but if she's a rescue, she is probably already very stressed out. She's been bounced around a lot and is no longer in an environment she feels safe in. Everything is new to her which can put pressure on an animal that has nearly lived out 1/4 of her life somewhere already. Especially with how much chinchillas rely on constant behaviors and schedules.
Be patient with her and be understanding of how scared and unfamiliar she is to everything. I'd suggest never grabbing her from her cage. What people say about talking to her while sitting by the cage and relaxing your hand in the cage are great. Just don't try to snatch her or chase after her. Her cage should be her "safe spot" so she always has a place to go to feel secure and calm herself down.
Let her decide when she wants out and when you first let her out, don't chase after her. If she's skittish, she'll probably find some place in the room to hide and will hide frequently. Again, let her have a "safe spot" that you never grab her from (unless you absolutely need to). This way if she gets scared when out playing, she'll always have a spot to feel protected in.
Follow a lot of the standard bonding tips from the guide posted earlier. (I have been following
this guide and my young guy is on his way to letting me pet him.) Just remember that it will probably take her longer than a young chinchilla to feel comfortable with you. Don't try to rush her and praise her for small victories. For example, you said she freaked out when you were changing her water bottle. Next time, if she remains calm, tell her how good she is.
As she warms up to you, you can start partaking in more bonding games. Personally, I took up reading to my chinchilla at night when it's time to go to bed. Sometimes if I'm reading something out loud to myself, he hops over and sits up to listen during playtime.