Are bed bugs able to live alone?

Yes bedbugs "are able" to live alone although that is very unusual. But if just one or two bedbugs hatch or are otherwise brought into a home, and then if the male bedbugs have no opportunity to contact any female bedbugs, the few bedbugs may remain resident in that home alone for an indefinite period. During that time they will almost certainly have meals of the blood of any human or humans sleeping in a bed in that home for perhaps years. But even if the home is not lived in by any humans or animals for a prolonged period, bedbugs can still survive alone without feeding therein for a year or more, unless discovered and exterminated.

But in most cases when bedbug eggs or live bedbugs first get into a residence there will be both male and female bedbugs in close proximity. So after a blood meal, and after being mounted by male bedbugs, the females will then lay eggs, e somewhere in or near the bed where the host sleeps. So after a week or so each batch of new eggs will hatch and hence new bedbug nymphs will be born. So the breeding will continue and multiply ad infinitum as the bedbug population gets larger and larger, until the infestation is discovered, dealt with and all the bedbugs and all their unhatched eggs are eventually destroyed.