How do I politely/non-awkwardly get to know/give my number to a woman on a bus, in a non-intrusive manner?

Question

So the title already gives some major details, but I’d like to evaluate further, to explain the situation better.

I’m currently working on a short-term job, ending next week. The commute to this workplace partly corresponds with that of said woman, though we board at different stops.

If you had to ask me what I know about her, I would have to admit that I know nothing. She seems interesting, dresses neatly, seems educated, and admittedly I like how she looks. So I’m judging a book by its cover, not knowing the contents. I know this may be pretty odd. But in any case, it would be nice to get to know her. Of course I realise that in doing so, my judgement may change and realise that we are simply very different.

Now, I want to do this in a very non-intrusive manner. Certainly not on the bus, with so many people around. We however get off on the same stop. Engaging in conversation on the bus is a no-go too, since she always has headphones on. Being in our 20s a note seems childish too.

Your opinions are highly appreciated! Cheers

Addition #1: I never successfully asked someone out directly. This makes me usually very nervous in a very obvious manner. Also, I’m leaving for a couple of weeks soon and when I return my commute may change (new job location etc) - so no guarantee that I’ll get many chances after next week! Maybe I should have though about this sooner...

Answer 1

It might be too late for this method, but this is usually how I end up "knowing" people that I initially only recognize by sight.

1. When eye contact is made, smile and nod hello/goodbye. No words. Works with headphones. Don't maintain eye contact for more than a second or two after the nod exchange.
2. When MUTUAL non-verbal greeting starts to occur; now you can start adding in words, "hello", "hiya". Eventually, ramp up to compliments and greeting-questions. "Hey, that hat is great!" "How are you today?" If she is wearing headphones all the time- this step may prove difficult- I've never tried, but I'd guess that trying to mime this stuff could be just as endearing. Just to clarify: it is not the intent to engage in conversation at this point, merely to exchange pleasantries.
3. If the person ignores you, well, then this method has failed. But usually, people will start to respond: After a few instances of this, the ice is broken; Attempting to engage in conversation with this person is now socially acceptable, and will no longer be considered intrusive.
4. At this point, it's time to simply ask her out. Keep it simple and make clear what you want. It sounds like just after exiting the bus is the best time. If you exit the bus first, just turn around and wait for her, then approach directly from her front, with a smile and small wave. Watch her face as you approach, this could clue you in that she does NOT want to interact. If it is clear that she does NOT want to approached by say.. avoiding eye contact - then don't, today is not the day. If she keeps up eye contact, maybe raising her eyebrows, you're good.
   I suggest simple wording like: "Hi. My name is Grey, and I would very much like to take you for a cup of coffee." Notice you haven't even asked her out here, you have simply stated what YOU wanted. She can now choose to go with you, or not, without being put "on the spot" to reject your offer.

Answer 2

I think you're going to have to step out of your comfort zone and directly approach her. The fact that you haven't previously, on a more casual level, in some manner, kind of puts you in this bind where you now need to be a bit more direct because of the time factor.

As a disclaimer, I'm very shy about approaching people, and this would definitely tie me into knots, and I'd probably wind up doing nothing except, later, thinking back wistfully on another opportunity passed by, but I find I have a lot more courage when advising others from behind my keyboard.

The approach I suggest is, just after exiting the bus, walk up to her, so she sees you coming, make eye contact, and if she still has the headphones in, give a little wave, while looking like you'd like to say something to her. If she removes the headphones just tell her -

1. You've been meaning to approach her and chat on the bus, but you're a bit shy and you didn't want to intrude.
2. Introduce yourself by first name, hopefully get hers in exchange, and offer a handshake.
3. You'd like to share a cup of coffee (or something casual) with her and get to know her a bit better.
4. Hopefully there's some kind of shop within a block or so of your bus stop, so there's a convenient and publicly visible location, to put her at ease about it.
5. Ask if she'd be interested, as a stop after work, and suggest a day very soon.

If she's not interested, thank her for her polite consideration and wish her a nice day. Accept the "no," if it's the reply, but hope, as we all will, that she will accept your offer for an ice-breaking beverage stop. Hopefully we'll see a "what in the world do I talk about on a casual 'date'?" question from you in the near future.

Answer 3

Considering the time issue, I have come up with the following solution based on the replies of @PoloHoleSet and @Glurth:

My next bus with her is on Monday, while my last bus is on Friday. Friday 7th I leave the country and return on the 20th.

1. Monday to Thursday I try to simply nod, and smile. When I sit next to her, I try to say hello or goodbye if the situation arises (i.e. if she doesn't have headphones on). So far, when she was looking at me I simply turned my head away, trying to avoid eye contact. I guess I didn't want to seem too obvious.

2. Based on the reaction I get from these subtle actions, I'll decide what to do on Friday. If she smiles back or nods, then I'll simply pass her a piece of paper with my number. I'm thinking of saying something along the lines of 'Hey, I'm Grey. I'd like to take you out for coffee when I return from [generic country] in two weeks time, if you're interested. Have a nice day!' - if she texts, then great. If not, then no problem I suppose; most probably I won't see her as often afterwards, even if we live in a small village.

Well...this will surely put my GAD treatment to the test. I'm nervous just thinking about it. Quite frankly I'm just afraid of the outcome - so many variables at play. Eg., will the fact that I'm asking her to meet me in two weeks time put her off? Or am I rushing things, trying to achieve a month's work in a week? I don't know...

All I know is that the last time I bottled up my feelings for someone, once I got to know her well things went south after a couple of years when we ended up living together under the pretence that we mutually viewed ourselves as just friends.