You might want to check out Bourdieu's admittedly limited work directly on gender, ie Masculine Domination, to see what he thinks might affect women's agency.

Suggested further readings:

https://www.jstor.org/stable/3685561?seq=1#page_scan_tab_contents

https://scholar.google.com/scholar_lookup?title=Cultures%20of%20Consumption%3A%20Gender%20and%20Home%20E-shopping%20in%20the%20Global%20Knowledge%20Economy&author=H.%20Richardson&publication_year=2005#d=gs_qabs&u=%23p%3DlGyts0-F2NoJ

Agency theory defines the relationship between the principal (shareholder) and the agent (directors), in which having more women as agents will have a lot of benefits in trying to reduce the agency cost. This is because woman have specific characteristics that could be useful which could be used in line to increase the shareholder's wealth. For example, woman are risk averse so they will question more as agents and challenge decisions proposed by male agents which will in turn reduce fraud, information asymmetry and reduce earnings management. Consequently, woman agents will stifle the creativity and the adventurous nature of male agents when venturing into new business ideas that are in line with the effort to increase shareholder's wealth. Woman agents are also meticulous in nature and are perfect to reside on the board audit committee when needing to challenge the CEO, CFO, external auditors and internal auditors.On the other hand, woman agents are sympathetic and have a lot of empathy when residing on the board nomination committee which in turn could select the wrong candidate for important posts due to having too much empathy in decision making.

Those are some examples on how the characteristics of a woman can have impact on the agency theory but they are not exhaustive.

A suggestion would be to look at prior studies on the specific characteristics of woman and how they would react in certain important situations that would have impact on the agency cost.