If you're linking in the MySQL libraries, well, that's linking as far as the GPL is concerned and you've created a derived work. See this question for example.
If you link to a GPL lib then you have created a derived work and your code must be GPL - this is different to LGPL code which specifically allows dynamic linking of differently licensed code. The system libraries including libc, are all LGPL.
Or here which quotes from the GPL FAQ
Linking [name of your program] statically or dynamically with other modules is making a combined work based on [name of your program]. Thus, the terms and conditions of the GNU General Public License cover the whole combination
In addition, see the Oracle MySQL licensing page, where this very issue is discussed:
A: Oracle makes its MySQL database server and MySQL Client Libraries available under both the GPL and a commercial license. As a result, developers who use or distribute open source applications under the GPL can use the GPL-licensed MySQL software, and OEMs, ISVs and VARs that do not want to combine or distribute the MySQL software with their own commercial software under a GPL license can purchase a commercial license.
So if you can find a BSD-licensed MySQL driver library, you can use it, but if you're using the libraries that MySQL provides, you either have to pay Oracle, or GPL your code.