Hey man, ive been there too, and im not always shy, just certain situations, like the one you told us about. I want to point out a few things to you to re-assure youself that you have the skill to get this girl's number ( which is what im recommending)
1. You were able to make her laugh - she was not laughing at your pathetic attempt to make a joke, come on, you are both college students and if some one laughs in college, a smart girl like the one u describe, most likely she is not lauging at you, becuase that is high school drama, shes laughing because your joke made her feel good.
2. She remembers your name (you even pointed this out) do you know how many guys hit on this girl a day? im sure she gets a lot of random guys attempting to hit on her and to her thats just some random face, soon to be forgotten, but since your friendly jokes make her giggle, she remembers your name.
3. Losers cannot make people laugh at their jokes. - losers are people that get laughed at because their life sucks. Your in college, that means you did well in highschool and you have a decent brain embedded in your puny skull. You are way above the ranking of a loser, that is just you doubting your own ablilites, trust me, if a cave man can get a girlfriend back in the day, so can you, and this is why you are going to get her phone number, because it will tell your (girl) friend that you are confident enough to tell her that you like her, even though your not actually saying " i like you" , which you dont want to do, trust me.
So how are you going to do it? simple, one day when you have a chat with her again, just say goodbye when your leaving her, and then say, oh wait can you write down your phone-number for me, and just hand her a pen and something to write on and i guarentee she will give you her number that easily. And if she asks why you want her number simply say " i enjoy talking to you and i would like to call you sometime" once again, it is that simple, women love attention.