Building a quality service-based system (SBS) is one of the most important research topics in software engineering. Many studies investigate intelligent methods to simplify the process of building SBSs. In particular, some keyword-based SBS building methods allow service users to automatically build an SBS by only providing a few of keywords. This type of work usually constructs a directed weighted graph of a service repository. A set of minimum-weight group Steiner trees (MSTs) is extracted from the graph to represent the service functions and their relations. However, to the best of our knowledge, none of the existing keyword-based SBS building methods allow the relaxation of the function requirements for a user. A relaxed SBS may achieve a comparable functionality versus a complete SBS containing all the query functions. To fill in the above gap, we define a new problem: a bounded skyline SBS building problem, whose solution is more adaptive and less limited than the traditional keyword-based SBS building methods. To solve this problem, we propose two algorithms based on skyline query, dynamic programming, and lower bound pruning. In the experiments, we collect real-world datasets and label the nodes with keywords. We conduct a comprehensive study to demonstrate the time efficiency of our algorithms on automatically finding SBSs. We make the annotated real-world datasets and our source code open to peer researchers.