The simple answer is that the faster you go the more effort/energy it takes but I would like to understand this in more detail, especially at relatively low speeds. Assume a flat smooth road and fix the bicycle and the person doing the riding. How does going at say 10, 15 or 20 km/h compare in terms of effort both per time and per distance?

The simplest physical model gives that the energy is proportional to the square of the speed but in that model maintaining a constant speed requires zero energy. To maintain constant speed in practice one needs to overcome friction of the bike and with the ground, the wind resistance and also invest some effort to keep the bike balanced and avoid falling over. How does friction scale with speed? Staying balanced gets easier with higher speed but are their formulas for that?

From personal experience (from riding with small kids) I have the impression that 15 or 20 km/h comes to about the same, so the extra speed doesn't seem to require extra effort. Going at only 10km/h seems to be more exhausting. I would like to understand whether there is some physical reasons for that or whether this is purely my subjective experience.