I am looking for a non hotel "extended stay" option for the area of
Wurzburg Germany.  Ideally it'd be an apartment or guest house for
30-60 days.  I can find lots of hotels, an hotel with a kitchen and
seperate bedroom would be ok, any option other than a standard hotel
room.

Dear GardnerVillian, 

There aren't so many hotels or apartment options in Wuerzburg, so I
apologise for the relatively short list.

Wurzburg's tourism site has an option to search for apartments and
pensions (guesthouses) in the town :
Wuerzburg Online - Hotels
<http://www.wuerzburg.de/hotels/> 

Since I couldn't really know when you're planning to stay, I put in a
random date, and extended the stay to 30 days - I got one apartment
hotel:

Hotel-Wohnungen am Spit?le 
<http://www.hw-am-spitaele.de/> 

Another place, this time a guesthouse/inn, is slightly expensive, but
received very good reviews at Frommers':
Zur Stadt Mainz
<http://www.frommers.com/destinations/wurzburg/H48730.html> 

A B&B is available here: 
bed & breakfast W?rzburg
Sigrid Schmidt-B?hr
Kaiserstra?e 6
97070 W?rzburg 
Tel.: (09 31) 40 45 60 9
Fax: (09 31) 40 45 61 0

You could try your luck in the area, where there are many holiday rentals: 
Ferienhaeuser (Holiday Rentals) in Wuerzburg and the nearby region
<http://www.tourist-online.de/overview.php?location=G7q3ZLg9t> 

(Because it says "Wurzburg", but also applies to the nearby region, I
would ask the owner how far it is in fact from the city centre, if it
matters).

Another possibility to rent an apartment is the HomeCompany, that
offers several apartments in the city:
HomeCompany, Wuerzburg
<http://wuerzburg.homecompany.de/jobberwohndb/suchmaske.php> 

Apartments are also available from Immowelt 
<http://www.immowelt.de/immobilien/IS_GeoSuche.asp?art=15&selgid=10809663> 
(You have to click on "Ergebnis Anzeigen" in order to see the apartments). 

And, similarly, from ImmobilienScout
<http://www.immobilienscout24.de/find.national/resultDialog.go;jsessionid=E7D88A8C9621E65E8CEE1BB08D773438.worker2?iac=0&style=is24&is24EC=IS24&pagerName.sortOrderList=Wohnart&pagerName.sortDirection=true&event%3AdoChangeSortOrder=sortieren>

If you come to the Wuerzburg University (or to the College of Applied
Science, the Fachhochschule), it could be much easier for you, as the
Student Union (Studentenwerk) offers dorms:
Dorms that belong to the Union
<http://www.uni-wuerzburg.de/studentenwerk/Wohnen/Wohnheime/wohn.htm> 

Dorms that do not belong to the Union
<http://www.uni-wuerzburg.de/studentenwerk/Wohnen/Andere/andere.htm> 

I hope this answers your question. Please contact me if you need any
clarification on this answer before you rate it. My search strategy
has been:
Wuerzburg (or Wurzburg) with the terms: 
Ferienwohnungen, Ferienwohnung, Ferienhaeuser, "auf Zeit", studentenheim

perhaps this might meet your needs??

http://www.pension-wild.de/#

or this one?

http://wuerzburg.homecompany.de/jobberwohndb/suchdetail.php?id=82984&pageNr=0

Gardner - thank you for the rating!