MPs on the committee did not recommend these changes, but they noted that bail laws had been tightened and made some recommendations to improve bail processes.
The committee's report said judicial accountability was a "complex and sensitive area'' and it was important the Parliament did not impinge on the judiciary's independence.
"On the other hand, the judiciary needs to be transparent and accountable for its decisions and the processes within its control, and to maintain a high degree of public confidence.''
The Chief Justice was already considering some changes, such as a new risk management tool for bail decisions and a peer review programme for judges' practice.
The committee said procedures should be established within the judiciary to analyse bail decisions critically when a released offender had committed a serious crime after their release.
It said consistency in bail decisions could be improved if, where possible, the same judge heard any further hearings on a bail application.
A recommendation was also made to consider allowing police to appeal bail decisions to the High Court.
Bail laws were amended earlier this year to extend the reverse burden of proof in bail decisions to 17-19 year-olds with a serious criminal record