Everything you bring into the Wilderness is "man's work."  That campsite is  as "noticeable" as a bike.  At least the bike just passes through (you know "where man is a visitor and does not remain" as stated in the Wilderness Act).  

"and invariably they come to the conclusion that bikes should stay out of the wilderness and other sensitive areas. "
That statement is unfounded and false.  There are land managers who have no objection to bikes in some wilderness, but they are hamstrung by a blanket ban that gives them no discretion.  Also, there are non-Wilderness sensitive backcountry areas that do allow cycling, so that also proves your statement false.  

If you'll "defer to their judgment," what do you have to fear from this bill?  According to you, their judgment would always disallow bikes, so you need not worry.  And if they allow bikes, then they have also exercised the judgment you are willing to defer to.