Has anyone written a letter introducing their new business to prospective customers? I'm want to get my name out to vendor/venues, but I'm struggling writing an "introduction" letter.

Dont say with words - Say it with CAKE!! I did some research into the number of employees at some local businesses ( banks, photographers, etc) places where lots of moms work. I took samples to those places with a few brochures and cards. It has turned into so many orders for practically pennies.

I agree with jenng, taking cakes directly to your potential customers is a great idea; but a bit tricky. You might want to call ahead and let office managers know you are coming. I can tell you some of the more popular places to drop off include:
Office buildings with relatively large numbers of staff; insurance agencies,
A large Medical Complex with a common area for staff
A college/university department i.e. School of Business
A college Alumni office, since they are often hosting galas and fund-raising
A car dealership that is open on a Saturday...what a great surprise
A spa or bed & breakfast
Deliver to a concierge, at a hotel that does not have a bakery i.e. like The W

Consider getting a stylish golf shirt with you bakery name and logo on it and make sure to have business cards because you never know who will be standing by watching you delivery the goodies. Good luck!