I have seen it bid as little as .10 for HWE but it doesn't mean the cheapest will get it, sometimes you can get the job by being comfortably in the middle or including more and explaining why you are a better choice. I dont do alot of commercial work anymore, but what usually works out the best for me is to give 2 or 3 different choices... a low bid to just pre-spray and extract, one with some added features - like a pre-vac & pre-scrub, and a "cadillac" bid with protector included.
Let them know that because YOU will supply drying equipment, your cleaning method will dry faster and be more convenient for them. Let them know that you will be happy to come back and re-treat or re-clean any areas they aren't happy with. If it is a nursing home, and you have done other nursing homes, talk about it with the customer so they will know you understand their problems and needs and you have the experience to deal with it.
Also, include a copy of your current insurance and workmans comp, I don't know how many jobs I got where the decision maker picked us because we did that. I had one building director say she was impressed because we were actually a "real business" because we included the insurance info before she asked for it.
Do you know for sure they picked a bid lower than yours? If that was the only reason they didn't go with you then you are probably better off for not getting the job because it will be another 5 years before they will do it again!