The accommodation page of the Dudley Metropolitan Borough Council (which is the source I used for my previous suggestions) lists B&Bs for each of the different areas administered by the council. However, for Dudley itself, there is just one B&B listed for the whole town. It's only got one double room and one single room, so you can see that not a lot of people want to stay in Dudley! (However, at �25 pppn, it's within your budget).
The B&B is here:
http://www.dudley.gov.uk/sys_upl/templates/PT_ Directory/PT_Directory_details.asp?esLtr=ALL&I temId=131994&action=Display&pgid=4490&tid=150& DirectoryKeywords=&CategoryID=26&Q312=Dudley&O rderDir=ASC&OrderFld=
The location is 1� miles from the bus station. If you need to plan a route, go to Multimap and enter DY2 7AD for the location of the bus station, and DY1 3DA for the B&B.
Searching under the category for 'Hotels, Inns & Guesthouses' doesn't bring up much either. (the few places offered are either too far out or too expensive). The best option is probably the Cottage B&B at the Lamp Tavern pub. It's 0.7 miles (10-15 minutes walk) from the bus station, but it's �35 per night (according to the council website)
http://www.bathams.com/dudley-accomodation.php
Chris