Objectively, are you a bit of a catch? Very good looking, charismatic etc?
If not, then my guess is she was joking and you are misreading her cues. As @tommy525 points out she’s taking an enormous risk here. In most large organisations a manager employee relationship would at the very least need to be declared to HR.
Maybe she’ll just review that job performance and not your salaried job.
I would say so.
Get a different girlfriend, then. One you don’t report to or work with.
She’s 30 and I’m 32. However, she looks older than me. She looks 35.
In my job, we generally don’t work with each other.
Now that we all know that formally means “formally” and not, as it appears we all thought, a typo for “formerly”… Treat it as a meal, not a date whatever her intentions may be. You should have never asked her out. I know someone who was in a relationship with his manager for about three years and, when the relationship turned south, his life went to hell. I believe she can also be fired for going on a date with you, so it’s very likely it’s just a meal to her anyway.
well that’s why whenever she sees me at work, she pretends she doesn’t see me.
It doesn’t matter. You’re in the same organisation.
Anyway, I’ve made my point.
I think that’s why she wants to be discreet about it.
She says the reason why she treats me differently at work is b/c she doesn’t want any gossip about us.
Having clarified formerly and formally, we need to clarify something else.
Having a meal with a co-worker is completely different from having a dinner! Is it dinner or a meal?
I asked her to have dinner with me.
Stop saying formally ffs. Learn some vocabularies.
and she changed it to: We can have a meal?
Anyways, bold move asking your female boss out for dinner!
I just said that we can have a meal together. I think she knew I was referring to dinner since it’s after work.
Her intentions are clear.
Could mean she dresses older to make people more comfortable about a young woman being the boss.
her face looks like that of a 35 year old.
Er… tell her that to end any possible thought of a relationship
ok my two cents purely based upon what has been written by yourself and others in this thread.
I have worked many years in companies in taiwan as well as american companies in the usa. And in the US if you date or want to date your manager that is a huge red flag and will likely result in both of you being replaced, not necessarily for that reason but they will get rid of you because the US is a litigious society. The company can be sued for “allowing” this to occur if one of the parties becomes aggrieved and claim sexual harassment. A Lose/LOSe situ for any American company. WE have to watch many videos on sexual harassment in the workforce. So basically do not date your manager or even say anything remotely of a sexual nature, especially if you are opposite sex.
Dating a coworker can also get you fired. Such is the USA. IN my former company a manager said a few things to a coworker who was not happy and reported to HR, who then basically dismissed both workers on the spot for review of their case (and reviews can be years long without pay ) so basically you are removed from your work and them without being officially removed.
She confided in me that our manager (Male) had asked her to walk around the facility just him and her to review her performance. She complained that such reviews should take place in the office not a walk around the facility. And he had asked her to bring her a cup of tea (shes asian from China) and she was incensed and complained to HR that she is not an assistant not one to be asked to bring tea!.
So next thing you know she comes to me and says to me she is not to discuss this matter with anyone and is to leave the premises immediately and she left. The manager also left immediately after getting a call from HR and he didnt look happy. They have never been back at that company.
I professed to know nothing when asked. and everyone who worked with both of them were asked for a statement as to what we saw or heard or think we saw, see no evil hear no evil assume no evil 
was my approach. Who me? I saw nothing, heard nothing and assumed nothing.
But here in Taiwan things are way more lenient. People have met many life partners at work. So dating is quite commonplace. Which does lead to jealousy and can lead to one or both of you being fired so heres my take.
Did you see TOP GUN??? Well if you didnt go see it. The first one not the second one.
Anyway its not the preferred situ but in taiwan it happens a lot even dating managers. Just make sure to “perform” or else she would feel she wasted her time with you and worse jeopardized her position by being with a loser
Also it is best to NOT say anything about a relationship with a TW girl. ALWAYS let her take the lead in “saying” what the relationship is and what it could become.
YOU just say NOTHING ABOUT that. just go with the flow is my advice unless you want it to end .
TW girls could sleep with you but if you mention she is sleeping with you …NOW the onus is on HER and shes the BAD GIRL.
So dont let her be the bad girl …you should always be the Big Bad Wolf (even if she is the one leading you on).
The little tigress sees you and wants to fling you about , she wants to play with you…big cat she is…
If it was me and I liked her A LOT i would go for it. Go whole hog, all the way the first day…take that girl by the horn (i mean hands) and frickin frick the shit outa her.
and say NOTHING about it. ZERO NADA. pretend nothing happened.