"bump, bump to top, back to top, or btt all mean that the person is responding to the thread primarily to move it back to the top of the forum listing.
The problem you're encountering where you get many unwanted results is a typical issue encountered with most search engines. A more full-featured search engine would provide a variety of techniques for refining the search but the TFL engine is more limited.
Sometimes it's possible to use an internet search engine and limit the options to only returns that come from a particular site. The internet search engines tend to have a lot more options for refining searches.
For example, you can type
site:www.thefiringline.com your search terms here
into the google search window. Then you can use google search refinement techniques to limit the results.