1. Ask about what equipment and supplies will be used during the cleaning process. Cheap vacuums don't do the job more expensive ones do. Hidden costs here could be lost time due to respiratory illnesses among your employees because cheap vacuums do not do a good job of removing contaminents from the carpet, and the cheap filters spew the rest into the air.
2. Good quality cleaning chemicals can keep your employee's illnesses down too. Don't be afraid to ask for literature on the chemicals to be used, especially for restrooms. We use Clorox Clean-up, which is awesome, for most surfaces.
3. Unfortunately, the use of undocumented workers is rampant in our industry. You do not want to be a participant in this illegal activity. Some janitorial service providers use this tactic in order to get lots of jobs through low-ball price bidding. Ask!
While totally understandable, and usually prudent, to seek out the lowest price, beware of the "too low" price. If you encounter a bid that is far lower than the others you receive, consider that a red flag and inquire further. Look at the companies that submitted the higher bids and check their references and BBB pages.