It all sounds great....and these are little flirtatious games you are both enjoying together. I think you are doing great and she is enjoying herself too. You can let this happen a bit longer and then get the strength to ask her out for some time just the two of you. I understand you are nervous, but what do you have to lose? If you ask and she says yes then, wonderful. If you ask and she says no, then you are in no different position than you are now. So, take a deep breath, enjoy what is building and when you are ready ask her if she would like to accompany you to dinner.
Wishing you the best. Let me know if I can help further, but if all good for now, please take a moment to click on the rating tab to rate my support. Thanks so much in advance.