The Battle of the Bulge - officially, the Ardennes-Alsace Campaign - and the Rhineland Campaign were two entirely different operations. There are two possibilities: your man participated but never recieved official credit (has been known to occur) or he embellished his role in the war (very common among veterans of all eras). War Department General Orders Numbers 33 and 45 of 1945 (GO #33 & #45, WD 1945) are the official bases for issuance of WWII campaign credits. The unit mentioned is that to which he was assigned while awaiting discharge. I can determine his overseas unit but it'll involve expenses that I'd have to pass along to you.
The best source for locating those he served with is the veterans association of his overseas unit (if, in fact, one was formed or still exists). Of course, you'd have to know that unit to determine this.