Does The Theme Changes effect the ranking?

Yes it's possible considering no two themes are the same which means your site structure and sitewide internal links will change.

Yeah it may be a factor but without seeing your site we can't help you much.

What exactly does changing your theme and bounce rate have to do with each other? ITS NOT YOUR THEME!

think this way.. Most wordpress sites have widgets for most recent posts or pagination or whatever.. Those would all link to other articles... but here is the catch. Someone clicks on an article for say something to do with "facebook" and all of your recent posts are about Twitter and reddit and whatever else.. people interested in "Facebook" are not going to care less about Twitter and reddit. You need to supply links based on page context to hopefully keep them on your site.

Something else to consider... looking at GA its going to count any visit that enters a page and then leaves the site ( single page visit ) as a "Bounce" There are a multitude of types of bounces.. if you are ranked on page 1 right now I would not be concerned. Bounce isn't always a bad thing...

You cant looked at any one single ranking indicator and lose a gasket because the number doesn't look right to you.. look at the overall picture... are you currently losing rank? is there a specific page that is getting more bounce than others?

Changing your theme because you have high bounce is CRAZY.... start on the micro side of the issue.. locate a possible problem page.. or as pointed out above.. adding some context based links into your posts. Work on the issue programmatically. Identify issues or potential issues and work through them one by one.

You may have a few problems.. but your theme aint one of them.