Be more independent than her. In the time you spend together give her reasons to like you, then make her work to have you around. Also dont push her in a direct sense...if she says she wants something, doesnt want something, is going somewhere, etc...dont argue, you wont win. Instead be crafty...imply changes, get her to think its her idea without coming across as spineless.
The best way to deal with independent people is to use their independence against them. Make them think its their idea, by using implications and suggestive communications.
You need to pike your battles, put your foot down when it really means something, but let it slide when it comes to the small stuff...as a matter of fact the less you care (and shrug off) the small stuff the more she will be to follow your lead.