Given a source relational database, a target OWL ontology and a mapping from the source database to the target ontology, Ontology-Based Data Access (OBDA) concerns answering queries over the target ontology using these three components. This paper presents the development of UltrawrapOBDA, an OBDA system comprising bidirectional evaluation; that is, a hybridization of query rewriting and materialization. We observe that by compiling the ontological entailments as mappings, implementing the mappings as SQL views and materializing a subset of the views, the underlying SQL optimizer is able to reduce the execution time of a SPARQL query by rewriting the query in terms of the views specified by the mappings. To the best of our knowledge, this is the first OBDA system supporting ontologies with transitivity by using SQL recursion. Our contributions include: (1) an efficient algorithm to compile ontological entailments as mappings; (2) a proof that every SPARQL query can be rewritten into a SQL query in the context of mappings; (3) a cost model to determine which views to materialize to attain the fastest execution time; and (4) an empirical evaluation comparing with a state-of-the-art OBDA system, which validates the cost model and demonstrates favorable execution times.