Methodological quality assessment is the critical thinking that you need to undertake when assessing a study. The assessment of risk of bias pushes you further to consider the 'so what' of the methodological issues you identify. The Cochrane Handbook is a really detailed guide describing bias and methodological assessment tools http://handbook.cochrane.org/
there are various publications, which deal with the compilation / development of systematic reviews. For your important question, I've chosen the following book:
Centre for Reviews and Dissemination, University of York (2009): Systematic Reviews: CRD's guidance for undertaking systematic reviews in health care. see: http://www.york.ac.uk/inst/crd/index_guidance.htm
You can buy this publication; or there's a free download available, see: http://www.york.ac.uk/inst/crd/pdf/Systematic_Reviews.pdf
According to this publication,"risk of bias assessment" is described as a necessary part of quality assessment (see chapter, 1.3.4, pp. 33-44). Performing quality assessment comprises the consideration of several factors like (see p. 33):
• Appropriateness of study design to the research objective
• Risk of bias
• Other issues related to study quality
• Choice of outcome measure
• Statistical issues
• Quality of reporting
• Quality of the intervention
• Generalisability
So the "risk of bias assessment" is just one part of this important process step, when performing systematic reviews.
The authors of the following publication describe the relation / connection between these two terms in the same way:
Shea, B.J., Grimshaw, J.M., Wells, G.A., Boers, M., Andersson, N., Hamel, C., & Bouter, L.M. (2007): Development of AMSTAR: A measurement tool to assess the methodological quality of systematic reviews. BMC Medical Research Methodology, 7(10). see the following links:
Perhaps you are interested also in the following publication, which deals with the topic "risk of bias" extensively:
Viswanathan M, Ansari MT, Berkman ND, Chang S, Hartling L, McPheeters LM, Santaguida PL, Shamliyan T, Singh K, Tsertsvadze A, Treadwell JR. (2012): Assessing the Risk of Bias of Individual Studies in Systematic Reviews of Health Care Interventions. Edited by: Agency for Healthcare Research and Quality Methods Guide for Comparative Effectiveness Reviews. AHRQ Publication No. 12-EHC047-EF. See the following links: