Hate to bring bad news, but that is definitely going to take a lot of customization coding (and experience to do so). Unless you are comfortable with digging right into code, this is one you either have to hire someone to do or hold off on this one. I can tell you, to achieve that result with a logo centered and a split menu on both sides is a lot more complicated than you might think.
That will still require some custom code changes to the header. Again, if you are comfortable with some code, you can try it, but you should also review Bootstrap version 2 on how the span containers the logo and nav are in…so you have some quick learning to do.
This actually brings me an idea for future themes of mine to include different header layouts, such as the default one, then another option setting to center the logo and nav, perhaps another layout, etc.
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