Michael is right in saying that you need to think about this before you ‘strike out on your own’. While you do not necessarily need to ‘overthink’ this, you need to consider the following questions:
Location: where is the studio? If you plan to train people out of your own home, are you compliant with zoning laws? If you plan to rent space, you NEED a detailed and formal business plan because you will have monthly cost no matter your income.
Insurance: you need professional liability insurance if you have your own business.
Exposure: this was really the question you were asking. Since you are new to the area, teaching classes at a well-regarded fitness club will give you great exposure to potential clients. Creating a professional image through a web site or using this portal here with IDEA FitnessConnect is another way to get yourself ‘out there’. You talked about a master instructor and PT. They may also be sources for referrals. Get shirts made with your business name and wear them wherever you go. Never leave the house without a business card.
Getting started is a challenge. Try to keep your operating expenses as low as possible until you have your feet on the ground on the income side.
I wish you good luck.