High attrition rates in science, technology, engineering, and mathematics disciplines are an ongoing problem. Graduate student attrition, in particular, is understudied. Most past studies have focused on students' attributes, undergraduate preparation, and mentoring relationships. Emerging results from the implementation of the American Physical Society Bridge Program (APSBP) suggest that departmental support structures could lead to increased retention. However, there are no validated instruments to measure students' experience of the departmental support structures. This paper describes the development and psychometric evaluation of the aspects of student experience scale (ASES). Items were developed based on prior literature and the APSBP recommendations, revised based on APSBP feedback, and subjected to psychometric evaluation. Principal components analysis of data from 397 students at 19 physics graduate programs (2 M.S. and 17 Ph.D.) across the U.S. resulted in four distinct factors: (a) mentoring and research experience, (b) professional development, (c) social and academic integration, and (d) financial support. ASES meets the standard criteria for divergent validity, discriminant validity, and internal consistency. Results of students' ASES response ratings are discussed, along with comparisons between students enrolled at APSBP and non-APSBP affiliated graduate programs. On average, we find that physics graduate students experience adequate mentoring and financial support; however, they report experiencing limited social and academic integration and a lack of professional development. We also find that students in APSBP affiliated programs report better experiences on all four factors than students in non-APSBP affiliated programs, with higher differences in social and academic integration and financial support. This study is a starting point for the refinement process of this instrument.