I doubt very much that bettas get lonely for each other's company in the same way that humans do. The very aggression of males alone should be enough of a tip-off that they do not crave each other's companionship, but rather view it as a threat more than anything. While females can get along in a large enough community, there will be a definite pecking order that is more military than social in structure.
I doubt that you need to worry about a lone male craving companionship; in fact, he may feel more secure and less threatened without another male nearby. If you're worried about exercise, the mirror is an excellent suggestion, as flaring promotes blood flow to his gills and can perk his interest as well.