The answer is yes to both questions: you do have to clear immigration in BOG, and you do have to take a shuttle bus to Avianca's "Puente Aéreo" domestic terminal. The connection is tight, but doable if your incoming flight is on time. Pay attention to Avianca personnel in the arrivals tunnel of the international terminal before immigration, who usually stand around and shout out connecting flight information (or just stand around...). They then usually lead you to the front of the line to clear immigration without a wait, and show you where to take the shuttle bus to the other terminal.

On the return, the process is similar, but easier since you have more time. When you arrive at the "Puente Aéreo" terminal, there is a connections counter right before baggage claim, where they will direct you to the shuttle bus to the international terminal.