There are several points to consider. First, just riding will accustom your back side to sitting on a narrow saddle. Secondly, rider weight is distributed to the contact points of the bike with some weight on the handle bar, some on the saddle and some on the pedals. To a large extent, comfort is a matter of finding the best distribution of weight on those points and this relates to bike fit. For example, if the saddle is to far forward there will be additional weight felt on the saddle. In this case, the saddle should be moved back. Most of us fiddle with saddle position until we find a good location. Lastly, saddles come in a large array of shapes to fit the large array of back sides. Generally, if the rider's position is rather upright, placing increased weight on the saddle, a wider saddle would be more comfortable. If the rider's position is more toward a racing position, lower, longer and stretched out, a narrower saddle would work better. Then there are all the positions in between with all the between saddle shaped.
For myself and many others, the process of finding a comfortable took some time and trials of 4-5 different saddles. With each different saddle I got a better idea of what to look for.