In practice, software engineers are only able to spend a limited amount of resources on statically analyzing their code. Such resources may refer to their available time or their tolerance for imprecision, and usually depend on when in their workflow a static analysis is run. To serve these different needs, we propose a technique that enables engineers to interactively bound a static analysis based on the available resources. When all resources are exhausted, our technique soundly records the achieved verification results with a program instrumentation. Consequently, as more resources become available, any static analysis may continue from where the previous analysis left off. Our technique is applicable to any abstract interpreter, and we have implemented it for the .NET static analyzer Clousot. Our experiments show that bounded abstract interpretation can significantly increase the performance of the analysis (by up to 8x) while also increasing the quality of the reported warnings (more definite warnings that detect genuine bugs).