[9YearLurker]

If one tenant brings in bedbugs that create an infestation, then, yes, you as the landlord are of course responsible not to have spread to the other tenants on your property.

[Sarcasm Factory]

No apartment-building landlord in his right mind will ignore a bedbug infestation. As you say, it can spread and drive out good tenants. But jumping to expensive whole-residence treatments is a last resort. Simple tools can often do the job. I only wrote about a few effective tools and a bit about their application. Much more can be said about tackling the problem, including bagging mattresses as pointed out by another fellow in this thread. You can buy special mattress bags or go redneck with duct tape and heavy-duty plastic garbage bags.

If one tenant brings in bedbugs that create an infestation, then, yes, you as the landlord are of course responsible not to have spread to the other tenants on your property.