Bigger than you might think.
Water is about 750 times more dense than air. This makes it a challenging medium to move through. As a result, practically all aquatic animals have streamlined bodies to make movement more efficient.
In terms of an existing biological model, the closest you will likely find is a remora hitching a ride on a manatee. This is a rare occurrence, but it has been known to happen. A typical remora is about 3 feet long and a typical manatee is about 10 feet. Scaling this up to a human rider, the mermaid would have to be approximately 20 feet long.
This is not a perfect model. A mermaid is not all that streamlined, and a person riding on a mermaid is even less so.
Additionally, having the rider above water presents another challenge. While an object is submerged in water, the water provides a buoyant force, effectively reducing the perceived weight of the object. If the rider was out of the water, the mermaid would have to constantly exert energy to keep the rider's full weight above water.
Fish control their buoyancy using swim bladders. To avoid too much math, let's assume both the human and the mermaid (with a deflated swim bladder) have a density that is equal to that of water. In this case, the mermaid would need to inflate its bladder to roughly the same size as the rider to maintain neutral buoyancy while supporting the rider above water.
Swim bladders are about one third the length of the fish they are a part of. This would require our hypothetical mermaid to be approximately 25 feet long.
Using both of these models, and factoring in some room for error, a good length to make your mermaids would be 30 feet.