I did as many others have said and shadowed my own doc. He was really great and has been very supportive of my education. As far as work day, I have that problem, too, not because I work, but because I'm home with my girls and my husband works. I just go in now and then on vacation days and such when it works out with both our schedule and my docs. He has also offered to call when he has ladie's in labor so that I can attend the births. This hasn't worked out schedule wise yet - but I'm looking forward to it!! Just so that you don't get discouraged if you get a no...I have also inquired with my daughter's pediatrician who gave me a flat out, "no." So, if you do get a no once, don't let that stop you from asking others. Some docs are more interested in helping premeds than others. I have found family practitioners to be quite open to the idea of premed shadowing. Good luck!
I was in a similar boat- here's what I did (when trying to shadow DO's)- just got the names and addresses of about 10 in my area of interest (FP)in my area on a directory of DO's on the web. I made up a cover letter explaining my interest in medicine and a brief background- basically why I wanted to shadow- along with my resume. I then sent them out, with plans to make a follow up call a week later. That way, they have an idea of who you are and your interest so its not so much of a cold call.
I was easily able to set up a shadowing appointment with several docs. Several of them called me first!