You should be paying $60 to $120 per hour for private lessons depending on the studio and location. At $120 / hour for 3 months (24 Private lessons) you would be paying $2800 which is top $ for your lessons in my opinion.
Going twice a week has nothing to do with preforming or competing. It has everything to do with practice, learning, comprehension, improving and everything else that a sport requires. Most sports require 2 to 4 hours per day. Could you learn how to play basketball once per week? Yes. It would take forever and you would stink at it.
However, taking one private per week, which they will allow you to do, taking all the group classes and dances offered will speed up the process. Taking 10 privates per week will do that as well but not a high percentage of people can afford to do that.
$200 20 years ago? Then you didn't take from the right people or studio. Private lessons were still $60 to $120 / hour. Group classes were still $7.50 to $10 / hour per person. More like $10 to $15 today.
Here are my suggestions. If you only want to take 1 lesson per week, then state that to the studio. Try other local studios in your area and see what they have to offer. If you find a location that offers instruction with 2 people teaching, go somewhere else. A Professional Instructor learns both sexes parts and has been trained to do both sexes part. Therefore, no need for 2 instructors during class. Less than $60 / hour for a private, probably should go someplace else. Less than $10 / hour for a group, probably should go someplace else.
By the way, good instructors cost money. Bad ones are a dime a dozen.