There are a few cases of Hermione flying on a broom herself - some we see directly, and some only referenced.
In Philosopher's Stone, twice in the last chapter:
They seized a broomstick each and kicked off into the air, soaring into the midst of the cloud of keys.
A few sentences later ...
Ron dived, Hermione rocketed upwards, the key dodged them both and Harry streaked after it ...
And finally, after the potion room, Harry tells her to go back, using the brooms:
... grab brooms from the flying-key room, they'll get you out of the trapdoor and past Fluffy - go straight to the owlery and send Hedwig to Dumbledore, we need him.
At the Burrow before school, in Half-Blood Prince:
He spent most of his days playing two-a-side Quidditch in the Weasley's orchard (he and Hermione against Ron and Ginny; Hermione was dreadful and Ginny good, so they were reasonably well matched) and his evenings eating triple helpings of everything Mrs. Weasley put in front of him.
I wouldn't count the escape from the Room of Requirement in Deathly Hallows, as she was on the back of Ron's broom rather than flying herself.