@jamsjames,
But you ARE trying to go on a date.
Trust me, people have better things to do than to think about whether one person is thinking about taking another person out. If they do think about it, they have nothing better to do and need to get a life of their own to mind.
Asking her out in front of a group would be awkward for her as that is a private thing.
Either catch her alone or if she's with a group quietly say to her you'd like to speak to her later. If some impolite nosy body asks you what you said, tell them it's private.
She's given you plenty of indications she's interested. It's your turn.
If she's not looking directly at you it may be she's shy or nervous about this too.