I'm using different IDE and Database Management System when I'm doing my Java projects, so I can only give you general ideas, which might be helpful (I hope so): I think your database runs as a service and a library is needed. Eclipse probably sees the service and links the libraries, when you build your project, these are used correctly when you start your project from Eclipse, but you want to use these without Eclipse, so, the main question I would ask myself in your place is:
"How does Eclipse run my project?"
If you find out the answer to this question and you run your project in the same way, your project should work just fine. When you build your project, does Eclipse tell you what command should be used to run the project in command line? If it does, then the solution is simple. I hope my ideas are helpful.