Adams was associate finance minister for the last year of the National Government. Adams also did stints as minister of justice, broadcasting, communications, courts, environment, social housing and social investment.
Bridges has said he intends to keep policies relating to social investment, National's programme of using in-depth and often personalised data to target at-risk and vulnerable people for support.
Adams stood against Bridges in the leadership contest and although the voting results are not known, Bridges has said he believed she had strong support.
It is understood finance was Adams' first choice of portfolio if she was not leader – and was her preference over becoming a deputy leader.
Others understood to be keen on the finance portfolio included Judith Collins and Jonathan Coleman.
Richardson delivered what she dubbed the "Mother of All Budgets" including massive cuts to the public sector and reforms which earned the nickname Ruthanasia.