it surprises me they don't ask for green cleaning
when I worked for local school district we easily came in under $.04 psf with 2, 2 man crews, 405 performers in 1 ton vans
everything was prevaced, nuke it and pull it, ran air movers but we didn't need to make a profit and sometimes it isn't about making a profit it is about keep employees and making money on the next job
so I guess the quote of, do you own a job comes into play
a second person can increase productivity anywhere from 25 to 50%
there is no mention about quality in your post so why would you try to bid quality, a lot of people already know what they are going to get when it comes to low bid
you might want to consider options to weigh the bid in your favor, a sq ft per hour cost slower pull vs faster pull = better cleaning, light chemical prespray vs heavy spray, prespray dwell time, etc, this is what we did when it came to gettiing some things we wanted vs a low bid item,
we wanted the 405 performers but there was only one supplier in the area and we needed 3 bids so we had the same guy submit bids from his store, corporate office and an out of state company