Is trust a 2 way street- Well in the idealistic world, trust should go both ways. But it does not always have a sense of reciprocity about it. Meaning, it does not always go both ways.
In "General" it is possible to trust someone that does not trust you. If we are just talking about "trust" on a day to day basis.
However, if you want to be honest, and let me know what exactly is going on, it would be much easier to answer the question.
Trust is a huge issue when it comes to a driver and spouse relationship.
Since I am not sure exactly what it is that you are referring to, I can only assume that the person "or in general" the subject is probably one that has been hurt over a period of time, and does not possess the inability to trust anyone or anything and is hiding behind a mask.
In other words, what has been done to this person is something that only a slow, gentle and loving hand will ever be able to over come.
With Strength, perseverance, understanding, sympathy, and a strong guiding hand it is possible that YOU can show this person that you deserve her/his trust.