The exploration of entrepreneurship has become a priority for scientific research in recent years. Understanding this phenomenon is particularly important for the transformation of entrepreneurship into action, which is a key factor in early-stage entrepreneurial activity. This gains particular relevance in the university environment, where, in addition to the conventional teaching and research functions, the entrepreneurial university operation based on open innovation, as well as the enhancement of entrepreneurial attitudes of researchers and students, are receiving increased attention. This study is based on a survey conducted among students attending a Hungarian university of applied science in Western Transdanubia Region who have demonstrated their existing entrepreneurial commitment by joining a national startup training and incubation programme. The main research question of the study is to what extent student entrepreneurship intention is influenced by the environment of the entrepreneurial university ecosystem and the support services available at the university. A further question is whether these factors are able to mitigate the negative effects of internal cognitive and external barriers by enhancing entrepreneurial attitudes and perceived behavioural control. The relatively large number of students involved in the programme allows the data to be analysed using SEM modelling. The results indicate a strong covariance between the perceived university support and environment among students. Another observation is the distinct effect of these institutional factors on perceived behavioural control of students.