Gender inequality in the arts is an international-scale issue, with mounting evidence suggesting that there are gender differences in the number of artists, their access to exhibition space in museums and galleries, and the volume and price of their sales on the secondary auction market. Here we leverage a massive longitudinal dataset, capturing the exhibition and auction sales of 56,678 gender-identified artists in 20,115 institutions. We confirm gender differences in population and access to exhibitions, with nearly 1.75 men for every women artist, an effect that increases for more prestigious institutions. Using this global population gender imbalance as a new baseline, we develop a measure of institutional bias that, combined with the network of artist trajectories, reveals systematic echo-chambers which limit the access for some artists to future exhibition opportunities. Finally, we demonstrate that the gender bias of institutions induces a strong gender difference in the access to the secondary auction market, with the most prestigious institutions enabling twice the access for male artists than for female artists. Taken together, this quantitative perspective of gender equality in art suggests that to establish gender equality in art, it is not enough to just increase the participation of women artists, we must break down these so called ``glass fences'' which systematically limit artist access based on gender.