What is a word or phrase that describes "a person who is having difficulty speaking with girls?"
"Shy" would be a description of someone who has difficulty speaking with people. You could describe someone as "Shy around girls", but knowing more about why they were shy might lead us to a better phrase.
I've seen in various old books (Vanity Fair, if I rightly recall) such a person described as a hobbledehoy, meaning an awkward, tongue-tied young man.
In psychology, Parthenophobia refers to an abnormal and persistent fear of virgins or young girls.
Someone who has difficulty speaking in stressful situations (such as the computer programmer and the girl) may be described as "tongue-tied".
How about "selective mutist", a selective mutist is someone who cannot talk in certain conditions, but is quite chatty in others. For instance, a boy at school having difficulty chatting with other girls, but when he gets home, jokes around a lot with his sister.
If that wasn't clear enough, how about "parthenophobic selective mutist"....
A geek or a computer geek could work for this kind of person.
"Painfully bashful" implies the person has a hard time talking or interacting with other people. "He was painfully bashful when in the presence of girls."
I would say Coy is related especially to Bashful/Shy - by not necessarily when talking to girls
This would be someone who chooses not to speak to women. Not out of fear or shyness but out of dislike. It has more of a negative connotation though.