While I realize that the carbon footprint of a bike isn't completely neutral, I don't believe that it's anywhere near 1/10 of that for a car.
My first thought is that that 1/10 of 1% would be high.
I looked at one of the papers authored by Shreya Dave. He makes attempts to formulate standards of Life Cycle Analysis for bikes and compare it to standard estimates for cars, but I'm thinking he makes a few assumptions that lead to a really high manufacturing and infrastructure cost for bikes. Assuming bike trail costs are proportions to car road costs when normalized for vehicle WIDTH, rather than weight. Mentioning, but then not calculating in, that short trip emissions for cars are about 40% higher due to start up costs, but not factoring that in the calculations (almost all bike trips substituting for a car trip would be "short trips" in car terms, yes?) There would be further "short trip " costs in manufacturing for cars, too - the wear cost per mile for short car trips is way higher than for highway travel.
Still the article changes some views I have. Even with the stuff I mentioned, the bike probably has a per mile footprint that is 2% to 6% of the footprint of a car.
Shockingly high for bike.