Hi Jeff, the document you mention probably just lists the units participating in the assault crossings of the Rhine. After the intitial assault crossings and the bridgehead expanded clearing the east bank of the Rhine, the front lines were many miles from the crossing sites and many more bridges were built at sites closer to the front to shorten supply lines & move followup units across the Rhine. These bridges got little or no mention or credit given to the units that built them, the assault bridges got all the ink and photos. So it`s entirely possible the 1010th did build a bridge accross the Rhine. If you can get the unit records from NARA, they`ll show the bridges built by them & where they were.
You`ll find information on the orginization of an engineer treadway bridge company in Field Manual 5 -5, Engineer Troops
Normaly treadway bridge companies were assigned or attached to armored divisions for river crossing working with the armored engineer battalions. In the case of the 1010th`s arrival dates they may have been under the command of ADSEC, ( Advance Section, Com-Z) but 12 Army Group Hqs would issue orders for bridge building.