TS,
You did well by throwing away your first chance .... If you really want something from her ....
Get her simple breakfast, something neat like a hushbrown or something, go up to her.
"I apologise for that day, i was feeling not so good. A little token, hope you accept my apologies" Then enough, no need talk too much and go back to your desk .....
I guess she will ask you for dinner within 2 days