1. A computer-implemented method, comprising: receiving, by one or more programmed computing systems that execute a software image execution service available to a plurality of users, instructions from one of the plurality of users to execute an indicated software image, the indicated software image including a defined file system and having associated bootstrap instructions that indicate a bootstrap image distinct from the indicated software image, the bootstrap image including a distinct file system that is not part of the defined file system; and executing, by the software image execution service, the indicated software image on behalf of the one user by: initiating the executing of the indicated software image on a host computing system, the executing indicated software image using the defined file system on the host computing system; under control of the host computing system, using the associated bootstrap instructions to load and execute the bootstrap image as part of the executing indicated software image, the loading of the bootstrap image including adding the included distinct file system as a new portion of the defined file system on the selected host computing system, the executing bootstrap image performing bootstrapping operations for the executing indicated software image; and after completion of the performing of the bootstrapping operations, continuing the executing of the indicated software image on the host computing system using the defined file system.