I agree that it's perfectly normal for her to be wary of your bedroom!
I think that the fact that every time she comes out you try and weigh her might contribute to her fear
As long as she's eating well and not ill, you don't need to worry about weighing her often, especially since she's not tame yet. Giving her time to just explore things at her own pace, even if she just wants to stay in one place, is best
Putting a playground on top of the cage, or even just a few perches on the outside of the cage so she has a place to sit near her "safe spot" can help her to explore, as can putting some exciting toys and millet out for her to check out on her own.
Also, it's fine to let Yuki out with her--they're already friends, right? Yuki may help her to get more comfortable with the outdoors, and it shouldn't be too hard to get them back in. Generally, they either go in at once together or you only have to get one inside when the other's already in
Although toilet paper rolls seem perfect for budgie toys, it's best to use paper towel rolls for those purposes as the toilet rolls have been in contact with the bathroom and may be contaminated with unsafe germs.
Best of luck! Jaeha will soon feel more comfortable in her environment, I'm sure.