The overall score and each of the line scores should be in your enlistment packet. If you want a copy you should be able to ask your Recruiter for it.
It used to take up to 2 weeks for MEPCOM to release the ASVAB scores as well as the Medical PULHES back into the USAREC computer system after the ASVAB and the Physical.
That was the 1990's, might want to ask your Recruiter how long it takes now.....time frames might be shorter now with more modern infrastructure they have post 2000 (heh-heh).
When I took my son to the NG armory for his test, he was given the scores that day. After everyone finished the test, they all just sat around waiting until the test administrator finished grading the tests. As she finished grading each one, she would give the scores to the recruiter who then took his/her candidate away with the scores. This was the result of a paper test.
Based on that, I would say it shouldn't take very long to have your scores. Since you took the test on Thursday then you should have the scores early this week, possibly as soon as tomorrow if the recruiter doesn't already have them.
Oh, that is good news to hear. He said he had to ship them to MEPS that day to get them graded. MEPS is only like an hour away from where I was so they probably got them friday or saturday. Thanks for the info.