Read a book a few years ago (though I think the book itself is more than tens years old) about a woman who captained her own starship and used some odd type of star travel that involved pretty much imagining the path and sending the ship down it. One of the first scenes is of her dumping her father's remains into the clouds of a gas giant.
It was a really odd book and I just cannot think of the name of it! Driving me crazy!
Sounds vaguely like the main voidhawk, a living starship named Oenone piloted by Syrinx. The ship is from Peter F. Hamilton's book The Reality Dysfunction, a part of the most excellent Night's Dawn Trilogy. Here is the wikipedia page of the plot.
Humanity has split into those who use a large amount of biotechnology (Edenists) and those who use more traditional technology (Adamists). It also features a Adamist who works in an orbital salvage job until he can afford to repair a ship.
From there the book becomes a galactic ghost hunt\war.
Ring a bell?
The detail about a woman burying her father's remains in a gas giant is in Redemption Ark by Alastair Reynolds, but I'm not sure the other details match.
This space travel sounds quite a bit like Five-Twelfths of Heaven by Melissa Scott. The remains thing doesn't match, but perhaps you picked it up from another book?
The space travel thing sounds exactly like how they travel in the Dune books by Frank Herbert.
One of the prequels by Brian Herbert describes the first experiments by a woman, I don't remember her name, but she worked together with I.V. Holtzman. And she preferred to take the journeys alone.
"The Ship Who Sang" by Anne McCaffrey involves a sentient starship (actually the human brain of a disabled girl installed as the ship's computer) attending a funeral service but I don't remember a gas giant being involved.
