Depends on situation
Situation 1You 2 are
very good friends and have known each other for a [color=redlong time[/color].

It is more likely she will accept your invitation to celebrate your b'day. Since she will definitely feel more comfortable gg out with u. Another point to note is, if you 2 are really good friends, she would most prob remember your b'day. Thus giving u a chance to invite her out. Maybe you can just ask her out for a meal when she calls to wish you or pass you your present.
Situation 2
You 2 are only so-so friends, but have known each other for sometime.

Maybe she might get suspicious about ur motives. Well....u still stand a chance.
Situation 3You have only known each other for awhile.

Maybe can try getting a few friends along too. So that she wont feel so awakward. Or u might risk her avoiding u in future if u come on as too strong and pushy or maybe she will feel bad for rejecting ur invitation. Since you 2 dun know each other well enof...it would be hard for either of u to try and clear up any misunderstanding under such circumstances, or, rather hard to make the other party accept your explaination readily.
** For all situation, Versatility is the word. Change according to how the situation changes.