Having a contact push your resume for a SA role

Hey guys,

So over the past couple of months I have made two solid connections in S&T at a BB, both invited me in to shadow them for the day and meet their analysts. We email regularly and casually, both are exec. directors and both have taken an interest in me, with one a desk that I am really passionate about (equity deriv trading because I am a math major).

My question to you monkey's is how do I go about emailing them to push my resume without it sounding like I have just been milking the connection for a resume push. I have a solid resume but I want to be sure, and also not offend these people because they are great people.

This is pertaining to a summer analyst role in S&T.