How do I get extracts in search results?
I think creating your own Twig filter is your best bet. 
So, create a filter that takes a string, searches that for another string and returns an extract. It could do this by using some regular expression hocus pocus, I guess.

{{ entry.bodyText | extract('your search term', 3, 3) }}


would be how you'd use it (assuming, for example, that your filter accepts the three arguments searchTerm, wordsBefore and wordsAfter).