Hello. Not sure if you're still interested in an apartment in Bernkastel-Kues as it looks like this is an older post, however, if you are here is a website for an apartment (actually there are 2 different apartments for rent in the same house so it may serve your purpose
it is on the Kues side of the river, not a bad walk to the Bernkastle side, there is parking available across from the house and it's possible to rent bicycles from a shop in Bernkastel if you'd like to take a nice ride along the Mosel to check out some of the other wine fests.
We stayed in the apartment Schlossberg several years ago and found it very reasonable, clean and nice. Just a note, the 2nd sleeping room in this apartment is very tiny so it may not meet your purposes.