Accurately bidding projects is a critical challenge for any customer oriented service company, and by coincidence, I'm in the midst of reading a book that talks about how to measure the cost of current projects and then use that data as a basis for accurately estimating future costs of similar projects / clients. (the book: All Your Money Won't Another Minute Buy, by Curt Finch).

To get started, you really need some initial data, so what I would do is find some potential clients who already have a cleaning service they use. Then go through their facility and measure their space. Estimate how much you would bid on the job, then ask them how much they pay. Most likely your bid will be low, probably too low. The question, then, is what aren't you considering when you measure and calculate costs? That's a key thing to figure out before you underbid a real job and lose your proverbial shirt on it.

If nothing else, it's always easier to lower your price after you get a job than to raise it. Customers rarely care that "it takes longer to vacuum than we thought" or "it's a nightmare to mop your granite stairsteps", but you'd produce goodwill if you came back after a few weeks (not one week!) and said "ah, appears we overestimated the time required by our team to clean your facility. We're gong to lower your rate 15% to reflect our growing efficiency as a cleaning agency."

Another idea: run an advert in the local business paper (or regular paper, depending on your desired clientele) and offer them a $5 Starbucks gift card for letting you bid on the cleaning job. Then make sure you call each of them afterwards and ask what the bids from other companies were too. A cheap way to collect competitive data. If you're paranoid you'll underbid, overbid each one deliberately, knowing that for your data collection period you won't land any jobs. You'll be able to calibrate your bidding against the winning bids and quickly zero in on the competitive market rate.

Also, remember that price isn't always the key deciding factor for a service company, even a cleaning service. You might highlight that you have bonded employees, for example, to give your clients a sense of security about their valuable data and equipment, or that you only use "green", environmentally friendly products for cleaning to protect the health and well-being of their workers.

Good luck, and do let us know how it turns out.