Hi avatarkim,
what version of jBPM do you use?
You should not use script tasks for interaction with a database. Use rather a service task and implement own handler. Script tasks are very simple, so service tasks can save you from many headaches with db interaction.
Regarding to your issues with MySQL driver - you should not upload the MySQL driver into Guvnor, only POJOs. What are you trying to achieve? If you are using JBoss AS/Wildfly, you should load MySQL driver as a module or a deployment. Do not include it in your application, or even upload into Guvnor. Also remember that Guvnor is only a repository, so I expect that you wanted to use jbpm console or own web application to run the process instances.
HTH