Much of this answer may be dictated by laws in your particular city, so check with your local business licensing agency for their requirements.
But generally, if you are only doing restorative cleaning and not any construction or demolition whatsoever, then the insurance is a lot like a janitorial policy and usually not very expensive. With that being said, there are a few things that may increase your premiums. The underwriter that your insurance agent goes to can also vary greatly from one to another, so be sure to look at more than one company for a quote.
The act of moving and keeping other peoples belongings in your possession at your facility is one of them. If you clean mold, or do forensic or water jobs, you may see an increase in your premiums. These types of jobs have higher risks involved than just a straight up garden variety fire job.
Others things that may affect your cost are your number of years in business, how many subcontractors you use, any prior losses on a business policy and if you have a recent bankruptcy or a history of bad credit.
Do your due diligence here and get several quotes and make sure that you’re properly covered and not just getting a cheap policy.