How hard is calculus for a kid who isn't mathy but is generally very bright?
Uhhh, she more that just "generally very bright" based on what you're saying. It sounds like you're seeing that she's not as "mathy" as she is other things, but that doesn't mean she's not mathy.
Calculus was the easiest math class I took in high school.
For me, algebra was hardest, and it got easier from there all the way through until I hit Fourier Series, where the combination of 8 am classes and a prof who talked like Grandpa Smurf got the better of me. I suspect, like everything else in this world, it depends upon how your brain is wired. Some kids latch onto arithmetic quickly but stall out when the abstract nature of algebra hits, while others see algebra as a huge relief from the difficulty of memorizing multiplication facts and computation algorithms.
I see the same with my advisees, many of whom come in taking pre-calc, and their math grades go up as they move into and through calculus.