Since I used to be a competitive bullseye shooter, having competed in many matches, shooting with people does not affect my shooting too much. Maybe if I have to shoot individually in front of a crowd, then yes, like most I get more nervous, until I actually start shooting. Then I just can zone in on my previous training and concentrate only on the sights.
Because I do shoot better than the average shooter, I either spend alot of time coaching, zeroing others guns or have people watching me shoot. So shooting with people is more a social thing, but for serious concentrate only on the thing at hand type training, I sometimes prefer to train by myself.
In fact I just got back from the range shooting with a newbie buddy. Spent about half my time helping him out, and the other half going through my scheduled drills. It does get lonely though, and it's not as fun when you shoot a tiny group, when there is no one to share it with!
Actually, I train 50% at least at home, dry firing and unloaded weapons draw and fire drills, reloads with empty mags, etc. For me, the firing range is only a way to show me that my at home, dry practice is being done correctly.