Well very common is to use the Big Five Personality questionnaire, they have five categories: Extraversion, Agreeableness, Conscientiousness, Emotional Stability/Neuroticism and Intellect/Imagination/Openness.
Please consider that trust is a very multi-dimensional and inter-related concept, therefore be sure if you really want to "try" to collect trust or more specific matters, such as openness.
As a general base to start your reserach have a look at this book (it is not the newest ne but a start to see where things are coming from): Measures of Personality and Social Psychological Attitudes
By Frank M. Andrews (see link)
Furthermore, please specify the domain you are testing in, becasue trust is very domain specific and normally not easily to generalise.
There is a Propensity to Trust Scale, sorry I do not have a link right now, but google will know. This scale looks how likely people are to trust sooner/more and it will shed light on how people answer further reust questions. E.g. If a person is generally not trusting anything and rates your e.g. Website as not trustworthy, then their propensity to trust might be a mediator of their rating of your website.
I know this is not exactly what you are looking for but it might be useful to include this as well on your study. Diffusion of innovations is a theory of how ideas and technologies spread though a society. http://en.wikipedia.org/wiki/Diffusion_of_innovations
I thank you very much for your support and insights.
Are you interested in a common “working paper” on the issue?
I have published articles and presented communication (most recently on 1-3 June in Geneva). I presented three sources of trust: the one who trust, the one who inspires trust and the one who enforce trust.
I am going to concentrate on each of them.
For the first one, personality of the one who trusts, we can prepare a common “working paper”, if you wish.