The Extra mod doesn't use a DLL and the I beleive the author has said he wants wants to keep it that way, so you'd be on your own.
If you don't try to merge in the various python things that come with BBAI, like the turn autorun, merging ought to be fairly easy. I haven't done a merge with a version newer than 0.80 but (assuming the basic structure of everything is the same) you should be able to get the main functionality by:
1) Copy the BBAI DLL (CvGameCoreDLL.dll) into the mod's Assets folder (no sub folder, directly in Assets).
2) Copy the BBAI GlobalDefinesAlt.xml into the mod's Assets/XML folder.
3) Copy the BBAI CIV4GameText_BetterBTSAI.xml into the mod's Assets/XML/Text folder.
That's probably all you need to get the main functionality. It leaves out some XML fixes (some of which might be in Extra already, I don't remember) and all the Python stuff, but it should make the AI smarter.