You should check with your local parks and recreation department. Many have facilities with pools that they lease to other groups,like swim teams and triathlon clubs. They will tell you what they require for such use.
And yes, you need to make sure that your insurance covers your using a pool. Most cover all that you do that is not outside your scope of practice. But the worst time to find out what isn’t covered is when it has already happened.
There is a chance that you could use a private pool, such as at an apartment or condo complex. But often these location are not willing due to increasing their potential liabiity.
Your task is more difficult than just looking for a fitness facility because there aren’t as many pools around as fitness centers/training studios. Also, your liabilities might be slightly different only because you are dealing with water. I’m not sure what the exact requirements are for holding a swimming class, but you will need to check with your local laws and regulations (if there are any) and your liability insurance. The best way to go about it, is to find a location that works for you and really ask them what their requirements are in order to let you conduct a swim class or start a small Club. I hope this helps.