Publishing a paper as the sole author (undergraduate)
It seems that it is not an ego issue for you even slightly and so if it's easier you might grease Professor B by offering him a co-author credit if he'll handle the revisions and creative changes you hint are needed.  If nothing else you will learn if he is missing the work ethic in addition to completely missing out on integrity already.

You might ask B if he would edit the paper and make the needed changes in exchange for a co-author credit.  As a courtesy you might also consider mentioning that idea to give Professor A a long distance call first so he won't be surprised by finding out about the two you you sharing credit and not including him after the fact.  Men of integrity are not missing from professional teaching completely but i wouldn't say they are not all that common either so I would want to grant him that small courtesy I think he is due.

Life can be easier when you let the Professor B's of this world help themselves to some of what is yours on occasion and getting in their way can make life unnecessarily complicated sometimes.

Then again sometimes telling them to stuff it is just too much fun to pass up.  (You end up having to deal with them anyway though, about every fourth time or so you can get knocked on your ass by these guys.  Either way you'll have done the right thing for at least one good reason.