As with any business, it will take time and a lot of persistence to grow it. You’ll hear a lot of “this won’t work” comments in any shape or form. Start small, get good at it and the word among studios will spread. You’ll need to to a lot of outreach at the begining and when somebody does need your services, be able to deliver.
Some places (larger gyms like 24 hr fitness, golds gym, etc.) are self suficient in terms of covering classes or have specific policies to follow (no outside instructors). however, there are other places (in fact I teach/train for one of them) that are open to having other instructors fill in in emergency / last minute situations or when there is no other instructor that is available to teach at a specific time.
All the best with your business and if you read this, shoot me an email. I teach and train in Orange County and LA area!