My male point of view tells me to advise you to let it go ...there is no point is pushing this any further, and also, there is no point in regreting something as casual as dogs barking at the moon ....you already appologized for the drunken-munkey late night phone calls, and you made your intentions on wanting to know her better, clear as daylight ....anything past that is called pushing, friend and it won't get you nowhere
In my opinion you are over reacting either over some girl to girl joke, either over something that never existed in the first place ...i mean, you and this girl you liked, didn't even had a date and you're talking about it like you just got dumped by your high-school sweet-heart ...i mean, cheer up man, there are plenty of fish in the sea outhere and your social ring extends beyond some prickster co-worker and her friend...so you are probably a bit shy and got scared when she called your name in a bar....so what ? it's not like you insulted the Queen of England , and she better know that bars/clubs/pubs = noise/loud noise/a lot of muffled voices, so if you really want to talk to someone you don't just yell his name , you go sit in their sight of view...anyway, you got dead drunk later on , and started texting/chatting them both while blood was in the booze (or the other way around)...again, it might be rude if you insulted them , but hey, it's not like capital punishment mistakes and you later appologized for it ....Let it be, stop pursuing this illusion, if she wants to get to know you better, she'll find a way to show it ....and my advice is to cut the intermediars also ...if you have something to say to somebody, do it yourself, not by other peoples mouth (i get it, you are a bit shy , no problem there friend...but it was unnecessary to ask your coworker for her permission to give you her number...think this girl never had guys hitting on her and asking for her phone nr before ? )
I get the feeling you are asking more about Dating 1.01/Seduction advices, rather then Breakup/Healing ones, and i hope i'm right ,because what you had can barely be called a "relationship", but it can be called a full "first date/first encounter miss fire"...So, no biggie if you're into dating tips, back to square one :
-as a general dating tip, it is a good thing that she offered an alternative to your midweek invitation (she didn't blow you right off the bat), but then again it's a major red flag that she played dead in the cornfield (aka radio silence) when the time to honour that invitation came -> Her words said "Sure", her actions said "Nope"
-again, as a general rule, after a push-away (the one above) the wisest thing to do is to react as nothing happened, show that her negative response didn't scratch your image or behaviour in any way-> there are other girls outhere, she's just one of the many
-now you might try to pursue this again, but doing it in the same way will lead you down in the mud for sure....i already mentioned that using a third person to intermediate a date is kind of a "No No" (it worked in mid-school and maybe junior high-school, and i know, women do this more then men do)...if you really want to try your luck again , you need to let a few weeks pass by (calling you a "nice guy" is not a good sign, trust me on that one ;) ), and then use a more "Manly" approach ...like calling her and asking her out for a cup of coffee/tea/whatever, no more coworker ...if she says "yes", you're good to go, if she says "No" or throws some excuses, count your losses and let her be ...it's not the end of the world , you know ? it doesn't mean that she's an evil monster/cruel woman/player, it just means she doesn't feel attracted to you ...there's no point in hating her/calling her names/building a grudge there