Just about every woman that uses any form of hair removal will get stubble down there. There's just nothing you can do about that. The only tips to help with stubble are to make sure you use a very good razor that gets a good close cut. Try experimenting with different types of razors. I personally cannot use the cheap razors down there because I cut myself. But with the more modern razors with multiple blades and flexible heads, I don't cut myself.
To avoid stubble, the best way to go is with waxing. I would recommend having it done professionally. It's a little embarrassing at first, but you soon get over it. The nice thing is that it's quick and you don't have to personally build up the guts to rip the hair out yourself. Haha! Waxing completely removes the hair and root so you will be without stubble until new roots start to grow in (which takes longer then if you shaved).