I don`t have experience with overseas manufacturing, but I can tell you a little bit about my experience with manufacturing in the U.S.A.
The most comprehensive source of U.S. manufacturers that I know of is ThomasNet (www.thomasnet.com). You can search by product name or material, as well as by state. All of the manufacturers I interviewed or visited were found on ThomasNet. It`s a great starting point. You`ll find that if you call a few of the companies you`re interested in, you`ll get a good sense of their willingness or ability to handle your project.
An internet search of sourcing information can easily turn up sites that list overseas manufacturers. I`m aware of alibaba.com, but there are many sites that offer sources for manufacturing in China.
Another avenue, depending on what material your handbag is made out of, could be the Trade Commission of Mexico. I found them to be eager for business and very helpful.
One piece of advise that I can offer - it pays to do a small production run in the U.S., as close to your location as possible, so that you can monitor the construction closely at first and iron out any unforeseen problems that crop up. Certainly it`s helpful to have good communication with the rep at the plant where your product is being made.
I`m still learning the ropes when it comes to manufacturing, but after a lot of patience and persistence, I have found an excellent company that is enthusiastic about my product, and very responsive in dealing with obstacles.
I hope this helps. Good luck to you!