I bike nearly 100% of my daily commute for the last 3 years. I am affected by traffic, not so much to the point that I am as slow as traffic, but traffic affects me to a discernable degree.
Bridge fail; increased load on bart.
Traffic jam == less aware driver which cause me to be more cautious on my route to work == slower...
I bike 2 miles from home to Bart, then bike 1 mile from Bart to office... used to be greater distance...
So minimum 6 miles a day: ~260 work days a year = ~1560 Miles biked... *3+ years at a scaling factor of say, 80% is ~3700 miles commuted... my speed has always been based on external factors; traffic, Bart death, cal-train fullness/death, weather, etc...
It is a significant impact on timing... so to say that Rush is not subject to any of this is ignoring reality.
HOWEVER: I will admit that in dense urban environ, with bikes, bike always win..
So: I'd conclude based on own experience that traffic reduction, sans massive catastrophe to the biker, is ~10-20% BELOW WHAT AN UNFETTERED BIKER CAN DO (i.e. n cars at all)
A biker, assuming reasonable distance, should be significantly faster than a car, in dense urban.