That's not what bypass ratio is, that's compression ratio. The bypass ratio is the volume of air channeled around the core divided by the volume channeled into the core. For a fixed core diameter, a higher bypass ratio by necessity entails a larger bypass channel which means a larger engine diameter.
You don't always need large-sized plumbing pipe to get more water flow. It can be achieved by simply building a higher water tower. A jet engine works the same way. You can use a larger single-stage fan to achieve higher bypass ratio, or use 2 or more stages of smaller fan to create higher pressure and speed of air flow inside bypass duct to get the same result. Even if the fan's diameter and stages are same, higher rpm will result higher bypass ratio. GE F-110 engine for instance: The size/diameters of -100, -129 and -132 variants are almost the same, but they have different bypass ratios.
Increasing the speed of air flow of bypass duct will reduce the fuel efficiency and make the engine more noisier. This is why civilian jet engines prefer single-stage fans. But a military engine may use the method if the diameter of the engine matters the most.