Fresh out of A&P school, you are not going to have the work experience to run an independent maintenance shop. I sure would be quite apprehensive to give my business to someone with no independent experience. Consider working for a GA shop for a couple of years and possibly get your IA before you shove off on your own.
A couple of years ago, a guy at KHEF Manassas, VA did what you propose. He started a mobile detailing business, provided some mobile maintenance and eventually provided maintenance as a sub-tenant of one of the FBOs. Unfortunately, he started cutting into the business of one of the other maintenance shops on the field and they bought his sublease out from the FBO effectively kicking him off the field.
The bigger the airport, the more paperwork and politics are involved to get started. Many airports have a 'uniform commercial standards' policy which is often slanted to protect the existing service providers. So dont be suprised if you go to the airport commission to get your business permit for a mobile aircraft detailing business and they require you to rent at least 5000sqft of space and provide a handicapped accessible toilet. The way to get around that is to work as sub-tenant of an existing airport business. So if there is an FBO that doesn't have maintenance, they may be interested in renting a little cubicle to you. They would get someone to call to change a customers tire or some sparkplugs and you would have a base of operations and a venue to advertise your services.
Otoh, if you go to a small place that doesn't have maintenance at this time, they may provide you with an office and a hangar in hopes of brining some traffic and fuel flowage.