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There are a number of papers that didn't use a Bayesian approach but provide a relevant basis for developing quantitative Bayesian models:
Zickar et al (2004) performed a mixed-model using item response theory to examine different classes of respondents to personality tests. While it doesn't appear to be a Bayesian analysis, it is an example of a more sophisticated quantitative model. Essentially it concludes that there is more than one type of "faking" process.
Komar et al (2008) performed a statistical simulation of the faking process that represented various mathematical models of faking. While this study wasn't Bayesian in approach and it didn't involve data collection, the mathematical models discussed are relevant in describing parameters of interest to a Bayesian model of faking (e.g., proportion of participants faking, average magnitude of faking, variability in magnitude of faking, etc.).
There are a couple of papers that I've found that have used a Bayesian approach to study faking.
Kuncel et al (2011) in their review article of faking detection techniques discuss a general approach for assessing honest responding originally presented by Prelec (2004) known as Bayesian Truth Serum. The approach involves asking respondents to indicate their own response to a question and to estimate the proportion of the population that would give the same response. If the respondent's estimate of the population proportion is greater than the average estimate, then the response to that question is expected to be more honest. The argument is that if we acquire our beliefs about the population from our experience, we are more likely to over estimate the degree to which the belief is shared with others because our experience is biased to include ourselves. See also this paper by Ray Weaver.
Ortega et al (2011) applied a Bayesian approach to faking bad in malingering contexts.
Komar, S, Brown, D. J., Komar, J. A., & Robie, C. (2008). Faking and the validity of conscientiousness: A monte carlo investigation. Journal of Applied Psychology
Kuncel, N. C, Bornemann, M., and Kiger, T. (2011). Innovative Item Response Process and Bayesian Faking Detection Methods: More Questions than Answers. New Perspectives on Faking in Personality Assessment
Edited by Matthias Ziegler, Carolyn MacCann and Richard Roberts.
Ortega, A., Wagenmakers, E.-J., Lee, M.D., Markowitsch, H.J., & Piefke, M. (in press). A Bayesian latent group analysis for detecting poor effort in the assessment of malingering. Archives of Clinical Neuropsychology. PDF
Prelec, D. (2004). A Bayesian Truth Serum for Subjective Data. Science, 306, 462-466. PDF
Zickar, M., Gibby, R. E., Robie, C. (2004). Uncovering faking samples in applicant, incumben, and experimental data sets: An application of mixed-model item response theory. Organizational Research Methods, 7, 168-190.