Re:
I would start with a free estimate or evaluation just to get my foot in the door and make a list as I do the walk-through of the things I saw "wrong", this can be around the computers, in the server room,etc. In any network, that's homegrown by the "locals", or an inexperienced tech, you will see something that needs attention. You can even make money, if they will let you, out of cable management around their computers or just dusting off desktops and laptops, to prolong their life.
Since they don't have someone, all you need is just to let them know that you are there for them; leave business cards, fliers, send monthly emails with deals (like 10/20% off your next call blabla). I leave a business card with everyone in the office or with the go to person for IT support, and this is someone that just replaced the toner in the printers but knows little about computers.
If you are shy, do it anyway, you will get over it in some time and with enough screw ups, you will learn from your mistakes and do it better in the future.
Good luck!