qqbot,
The non-neediest way to make her your girlfriend (and the way we recommend doing it on this website)
is to let her bring it up to you.
If you continue seeing the girl rather regularly (at least once or twice a week), and you continue to have sex and meaningful conversation with her,
eventually she'll be the one to bring it up to you in one form or another. From there, it's just a matter of having an attitude of "I guess we can try that out for a bit and see how it goes" toward it. She'll probably be ecstatic about it.
There's nothing more non-needy than not bringing it up at all!
- Franco