I believe that this would fall under General liability insurance.
Usually for airplanes, your coverage limit would have to be at least 1 milion, and depending on the client, they may require you to have a higher limit wich would then fall under an umbrella policy which is usually 5 million. That will bring your total coverage for loss to 6 million should anything happen to the plane or planes your working on.
If you are the boss/owner, then you would also be required to carry Workers comp insurance unless you "hire" your other workers as sub contractors, then they would have to carry their own workers comp and insurance coverage.
Also, if your cleaning the outside of the planes, the airports usually have a special area to do this as the water run off can contain harmful chemicals to the environment such as de-icing chemicals etc. the water run off is usually caught in a basin where it will then be filtered, then turned into clean water, and if this is the case, you may also need to purchase an environmental policy too.
Theres allot to it and im probably leaving out some small details, but thats what I got from the insurance gurus here at work
Lastly, if you search online, there are associations that you can join for this type of business that offer discounts on your insurance premiums because it would be a group buy. You might want to look into this seeing where your just starting off and the insurance premiums can be in the thousands for all of the coverage you would need.