Here is an article by ACE about music licensing that may also help you…
(answer regards the United States. Other countries’ laws are very different!)
Your best bet for this, although you won’t like my answer, is to hire an entertainment attorney.
When there is a public performance of music (and playing music in a group-ex setting is a “public performanc”), ASCAP, BMI, and SEASAC will want a cut so that they can compensate the original artists. It’s based on the number of classes that will be held and the expected (new class) or average (existing class) attendance. If it’s a gym or a ballroom, usually the facility pays the fees.
It’s not easy for an independent instructor to get an individual music license, but it is possible. You could contact each of the above agencies individually before hiring an attorney, but the people I know who teach independently as their primary livelihood and do traveling masterclasses have taken the step of hiring one. The fees can be very large if done wrong.