Are search engines going to see my dynamically created content in Bootstrap tabs?

No, we (Google) won't see the content behind tabs iff the content under the tab is dynamically generated (i.e. not just hidden).

You can also see what we "see" using Fetch as Google in Search Console (former Webmaster Tools); read more about the feature in our post titled Rendering pages with Fetch as Google.

The best aproach is to design the website to work without javascript, and just replace all your anchor elements that work with ajax to pass a GET variable to your web controller, so it knows to return just the html to be inserted with javascript.

If you are using JS/AJAX, (I don't really see any, but I can't think of a better alternative) you are going to have a hard time getting Google to index your pages. Google has a good documentation on this that has helped me in the past on projects with similar goals.

https://developers.google.com/webmasters/ajax-crawling/docs/learn-more

Is it really that big of a deal to not load the content until the tab is clicked? Unless you are working with an un-cacheable constantly updating database and massive HTML output that would create a long flash of unstyled content I would say splitting the tabs view code is somewhat trivial.