In general it's a good thing to separate servlet from the jdbc/database related code.
I think it's better to define and use dbPath and conn only as local variables (inside the methods), and then you don't have to worry about synchronization.
on't return the resultset to the servlet: -a servlet is for request/response, and should not have knowledge about how you store you data (rel. database or files or whatever) -make sure you always close your connections, statements and resultsets (do it in a finally block)
One more tip: try to use connection pooling (with a datasource). It's faster and makes your code less dependant on a particular driver.